Elementary School Math Quiz: Find Factors And Identify Primes
19 questions · exam conditions
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Find Factors And Identify PrimesQuestion 1 of 19

Consider the numbers 77, 79, 81, 83. How many of these numbers are prime?

Exactly 1 number is prime in this set
Exactly 2 numbers are prime in this set
Exactly 3 numbers are prime in this set
All 4 numbers are prime in this set
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Elementary School Math Quiz

Elementary School Math Quiz: Find Factors And Identify Primes

Practice Find Factors And Identify Primes in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Find Factors And Identify Primes, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Consider the numbers 77, 79, 81, 83. How many of these numbers are prime?

  1. Exactly 1 number is prime in this set
  2. Exactly 2 numbers are prime in this set (correct answer)
  3. Exactly 3 numbers are prime in this set
  4. All 4 numbers are prime in this set
Explanation: Checking each number, 77 (7 x 11) and 81 (3 x 3 x 3 x 3) are composite, while 79 and 83 have no factors besides 1 and themselves, making them prime. So exactly 2 numbers in the set are prime. The other choices come from missing one of the composite numbers or misclassifying a prime number as composite.

Question 2

A factor is a whole number that divides another number evenly (with no remainder). List all the factors of 4545.

  1. 1,3,5,9,15,451, 3, 5, 9, 15, 45 (correct answer)
  2. 1,3,5,9,451, 3, 5, 9, 45
  3. 3,5,9,15,453, 5, 9, 15, 45
  4. 1,5,9,10,15,451, 5, 9, 10, 15, 45
Explanation: The factors of 45 are 1, 3, 5, 9, 15, and 45, since each of these divides 45 evenly with no remainder, making Choice A correct. Choice B leaves out 15, which also divides 45 evenly. Choice C leaves out 1, even though every number is a factor of itself and of 1. Choice D includes 10, which does not divide 45 evenly and is not actually a factor.

Question 3

A factor is a whole number that divides another number evenly (with no remainder). List all the factors of 6464.

  1. 1,2,4,8,16,32,641, 2, 4, 8, 16, 32, 64 (correct answer)
  2. 2,4,8,16,32,642, 4, 8, 16, 32, 64
  3. 1,2,4,8,16,641, 2, 4, 8, 16, 64
  4. 1,2,4,6,8,16,32,641, 2, 4, 6, 8, 16, 32, 64
Explanation: This question tests 4th grade ability to find all factor pairs for whole numbers 1-100, recognize that a number is a multiple of each of its factors, determine if a number is a multiple of a given one-digit number, and determine whether a number is prime or composite (CCSS.4.OA.4). A factor is a whole number that divides another number evenly with no remainder—if a × b = n, then both a and b are factors of n, and (a, b) is a factor pair. To find all factor pairs, systematically check: does 1 divide n? does 2? does 3? and so on up to √n, stopping when factors start repeating. A prime number has exactly 2 factors (1 and itself), while a composite number has more than 2 factors. The number 1 is special—it's neither prime nor composite (only 1 factor). For the number 64, to find all factors: systematically check divisibility starting from 1 up to √64=8: 1,2,4,8,16,32,64 (all powers of 2). Choice A is correct because all factors are listed (checked all numbers 1 through 8, and beyond via pairs) and none are missing or extra, demonstrating systematic factor finding and understanding of prime/composite definitions. Choice B represents including non-factors, which happens when students include numbers that don't divide evenly like 6 (64÷6≈10.666). To help students: For finding factor pairs, use systematic approach—start with 1 (always works), check 2, 3, 4, 5, etc., stop when you start seeing the same pairs reversed. Example for 24: 1×24 ✓, 2×12 ✓, 3×8 ✓, 4×6 ✓, 5 doesn't work, 6×4 (already have 4×6, stop). For prime/composite, count factors: exactly 2 = prime, more than 2 = composite. Remember: 1 is neither (only 1 factor), 2 is only even prime. For multiples, divide: if no remainder, it IS a multiple (48 ÷ 6 = 8 R0 ✓). Use arrays to visualize: 12 objects can arrange as 1×12, 2×6, 3×4—each arrangement shows a factor pair. Connect: if f is a factor of n, then n is a multiple of f (inverse relationship). Watch for: missing factor pairs, including non-factors, calling 1 prime, thinking all odd numbers are prime (9, 15, 21 are composite), confusing factors with multiples, and not checking systematically.

Question 4

A factor is a whole number that divides another number evenly (with no remainder). Determine whether 2929 is prime or composite.

  1. Prime, because its only factors are 1 and 29 (correct answer)
  2. Prime, because all numbers are prime
  3. Composite, because it has factors 1, 2, and 29
  4. Composite, because it is an odd number
Explanation: Prime is correct because the only whole numbers that divide 29 evenly are 1 and 29. The second choice is incorrect because not all numbers are prime. The third choice is incorrect because 2 does not divide 29 evenly. The fourth choice is incorrect because being odd does not determine whether a number is prime or composite.

Question 5

A factor is a whole number that divides another number evenly (with no remainder). Which numbers are factors of 3636 from this list: 5,6,8,95, 6, 8, 9?

  1. $6, 8,$ and 99
  2. 55 and 88
  3. 66 and 99 (correct answer)
  4. $5, 6,$ and 99
Explanation: Checking each number, 36 divided by 6 is 6 and 36 divided by 9 is 4, so both divide evenly, while 36 divided by 5 and 36 divided by 8 both leave remainders, so only 6 and 9 are factors, making Choice C correct. Choice A incorrectly includes 8, which does not divide 36 evenly. Choice B, 5 and 8, includes two numbers that are not factors of 36 at all. Choice D incorrectly includes 5, which also does not divide 36 evenly.

Question 6

Which numbers are factors of 40? Check 5, 6, 8, and 10.

  1. 5, 6, 8, and 10
  2. 5, 8, and 10 (correct answer)
  3. 6 and 8 only
  4. 5 and 10 only
Explanation: The correct answer is B because 40 divides evenly by 5, 8, and 10, but not by 6. Choice A wrongly includes 6, which does not divide 40 evenly. Choice C picks 6, which isn't a factor, and leaves out 5 and 10, which are. Choice D leaves out 8, which is also a factor of 40.

Question 7

A factor is a whole number that divides another number evenly (with no remainder). Find all factor pairs for 2424.

  1. (1,24),(2,12),(3,9),(4,6)(1, 24), (2, 12), (3, 9), (4, 6)
  2. (1,24),(2,12),(3,8),(4,6)(1, 24), (2, 12), (3, 8), (4, 6) (correct answer)
  3. (1,24),(2,13),(3,8),(4,6)(1, 24), (2, 13), (3, 8), (4, 6)
  4. (1,24),(2,12),(3,8)(1, 24), (2, 12), (3, 8)
Explanation: The complete factor pairs for 24 are (1,24), (2,12), (3,8), and (4,6), since each pair multiplies to 24. Choice A includes (3,9), but 3 times 9 is 27, not 24. Choice C includes (2,13), but 2 times 13 is 26, not 24. Choice D is missing the pair (4,6), so it isn't complete.

Question 8

A factor is a whole number that divides another number evenly (with no remainder). Find all factor pairs for 4545.

  1. (1, 45), (2, 22), (3, 15), (5, 9)
  2. (1, 45), (3, 15), (5, 9) (correct answer)
  3. (1, 45), (3, 15)
  4. (1, 45), (5, 9), (9, 5)
Explanation: (1, 45), (3, 15), (5, 9) is correct because these are all the whole-number pairs that multiply to 45. The first choice is incorrect because it includes (2, 22), and 2 does not divide 45 evenly. The third choice is incorrect because it is missing the pair (5, 9). The fourth choice is incorrect because it lists (5, 9) and (9, 5) as if they were different pairs, while leaving out (3, 15).

Question 9

A factor is a whole number that divides another number evenly (with no remainder). List all the factors of 2020.

  1. 1, 2, 4, 5, 10, 20 (correct answer)
  2. 20, 40, 60, 80
  3. 1, 2, 3, 4, 5, 10, 20
  4. 1, 2, 4, 5, 20
Explanation: The correct answer is 1, 2, 4, 5, 10, 20, because each of these numbers divides 20 with no remainder. Choice B, 20, 40, 60, 80, lists multiples of 20 instead of factors. Choice C, 1, 2, 3, 4, 5, 10, 20, mistakenly includes 3, which does not divide 20 evenly. Choice D, 1, 2, 4, 5, 20, leaves out 10, which is also a factor of 20.

Question 10

A mystery number between 4040 and 5050 can be written as the product of exactly two prime numbers, and the two primes may be the same number used twice. Which numbers could be the mystery number?

  1. 4141 and 4343 are the only possibilities
  2. 4646 and 4949 are the only possibilities (correct answer)
  3. 42,44,45,46,4842, 44, 45, 46, 48 are all possibilities
  4. 4747 is the only possibility in this range
Explanation: The correct answer is B because 46=2×2346 = 2 \times 23 and 49=7×749 = 7 \times 7, each written as a product of exactly two prime numbers. Choice A picks 41 and 43, which are themselves prime and can't be written as a product of two primes. Choice C includes several numbers, like 42 and 45, that are products of three or more primes. Choice D leaves out 46 and 49, which also fit the description.

Question 11

A factor is a whole number that divides another number evenly (with no remainder). Is 5151 prime or composite? Use the number of factors to decide.

  1. Prime, because its only factors are 11 and 5151.
  2. Composite, because 5151 has factors other than 11 and 5151. (correct answer)
  3. Composite, because all numbers over 5050 are composite.
  4. Prime, because 5151 is an odd number and odd numbers are never composite.
Explanation: The number 51 can be divided evenly by 1, 3, 17, and 51, so it has more than two factors and is composite, making Choice B correct. Choice A is wrong because 51 has more factors than just 1 and 51. Choice C uses a false rule, since being over 50 has nothing to do with whether a number is prime or composite. Choice D is wrong because being odd does not determine whether a number is prime or composite; 51 is odd and still composite.

Question 12

A factor is a whole number that divides another number evenly (with no remainder). 1212 objects can be arranged into rectangular arrays. Which list shows all possible arrays?

  1. 1×12, 2×6, 3×41\times 12,\ 2\times 6,\ 3\times 4 (correct answer)
  2. 1×12, 2×61\times 12,\ 2\times 6
  3. 1×12, 2×5, 3×41\times 12,\ 2\times 5,\ 3\times 4
  4. 1×12, 2×6, 4×31\times 12,\ 2\times 6,\ 4\times 3
Explanation: Testing whole numbers against 12 shows the complete set of arrays is 1×121\times 12, 2×62\times 6, and 3×43\times 4, counting each array once regardless of orientation. Choice B leaves out the 3×43\times 4 array, so the list is incomplete. Choice C includes 2×52\times 5, but 2×5=102 \times 5 = 10, not 12, so that pair is not a valid array. Choice D repeats the 3×43\times 4 array in reverse order as 4×34\times 3 instead of listing each array once. Choice A lists every true array for 12 objects exactly once.

Question 13

A factor is a whole number that divides another number evenly, with no remainder. Jamal arranges 1818 tiles into equal rectangular arrays. Which list shows all possible arrays?

  1. 1×18,2×9,3×61\times 18, 2\times 9, 3\times 6 (correct answer)
  2. 1×18,3×6,4×51\times 18, 3\times 6, 4\times 5
  3. 1×18,2×9,6×3,9×21\times 18, 2\times 9, 6\times 3, 9\times 2
  4. 1×18,2×91\times 18, 2\times 9
Explanation: The complete list of factor pairs for 18 is 1×181\times18, 2×92\times9, and 3×63\times6, every pair of whole numbers that multiplies to 18. Choice B includes 4×5=204\times5=20, which is not 18, so that pair is invalid. Choice C repeats the same arrays in reversed order (6×36\times3 and 9×29\times2) as if they were additional, different arrays, when a 3×63\times6 array and a 6×36\times3 array are the same rectangle turned sideways. Choice D is missing the 3×63\times6 pair.

Question 14

A factor is a whole number that divides another number evenly (with no remainder). Find all factor pairs for 2828.

  1. (1,28),(2,14),(4,7)(1, 28), (2, 14), (4, 7) (correct answer)
  2. (1,28),(2,14),(3,9),(4,7)(1, 28), (2, 14), (3, 9), (4, 7)
  3. (1,28),(2,14)(1, 28), (2, 14)
  4. (1,28),(2,14),(4,7),(7,4)(1, 28), (2, 14), (4, 7), (7, 4)
Explanation: The correct answer is A because the complete factor pairs of 28 are (1,28)(1, 28), (2,14)(2, 14), and (4,7)(4, 7); every whole number that divides 28 evenly appears once in this list. Choice B wrongly includes (3,9)(3, 9), since 3×9=273 \times 9 = 27, not 28. Choice C is missing the pair (4,7)(4, 7). Choice D lists (4,7)(4, 7) and its reverse (7,4)(7, 4) as if they were two different pairs, when they represent the same factor pair written in reverse order.

Question 15

What is the remainder when 6363 is divided by 88?

  1. 0
  2. 7 (correct answer)
  3. 1
  4. 5
Explanation: Dividing 63÷863 \div 8 gives 77 with a remainder, since 8×7=568 \times 7 = 56 and 63−56=763 - 56 = 7. Since there is a nonzero remainder, 8 is not a factor of 63, so 63 is not a multiple of 8. Choice A would mean 63 divides evenly by 8, which it does not. Choices C and D are incorrect remainders.

Question 16

A factor is a whole number that divides another number evenly (with no remainder). Which of these numbers are factors of 4242: 3,5,6,73, 5, 6, 7?

  1. 33 and 55
  2. 55 and 77
  3. $3, 6,$ and 77 (correct answer)
  4. $3, 5,$ and 66
Explanation: The correct answer is C, 3, 6, and 7, because each of these divides 42 evenly (42÷3=1442 \div 3 = 14, 42÷6=742 \div 6 = 7, 42÷7=642 \div 7 = 6). Choice A includes 5, which does not divide 42 evenly. Choice B also includes 5 and misses two true factors. Choice D includes 5 along with two correct factors, so it is not a complete or accurate list.

Question 17

A factor divides a number evenly, with no remainder. Find all the factor pairs for 4949.

  1. (1,49)(1, 49) only
  2. (1,49)(1, 49) and (7,7)(7, 7) (correct answer)
  3. (1,49)(1, 49), (7,7)(7, 7), and (2,24)(2, 24)
  4. (7,7)(7, 7) only
Explanation: The factor pairs of 4949 are (1,49)(1,49) and (7,7)(7,7), since 1×49=491 \times 49 = 49 and 7×7=497 \times 7 = 49, and no other whole numbers divide 49 evenly. Choice A lists only one of the two pairs. Choice C adds (2,24)(2, 24), but 2×24=482 \times 24 = 48, not 4949, so 2 is not a factor of 49. Choice D lists only the repeated-factor pair and leaves out (1,49)(1, 49).

Question 18

A factor is a whole number that divides another number evenly (with no remainder). Find all factor pairs for 6464.

  1. (1, 64), (2, 32), (4, 16), (8, 8) (correct answer)
  2. (1, 64), (2, 32), (3, 21), (4, 16), (8, 8)
  3. (1, 64), (2, 32), (8, 8), (16, 4)
  4. (1, 64), (2, 32), (4, 16)
Explanation: Testing whole numbers against 64 shows the complete set of factor pairs is (1, 64), (2, 32), (4, 16), and (8, 8). Choice B includes the pair (3, 21), but 3 times 21 equals 63, not 64, so that pair does not belong. Choice C repeats the pair (4, 16) in reverse order as (16, 4) instead of listing it once. Choice D leaves out the pair (8, 8), so the list of factor pairs is incomplete. Choice A lists every true factor pair for 64 exactly once.

Question 19

A factor is a whole number that divides another number evenly (no remainder). List all the factors of 1818.

  1. 1,3,6,91, 3, 6, 9
  2. 1,2,3,6,9,181, 2, 3, 6, 9, 18 (correct answer)
  3. 1,2,3,4,6,9,181, 2, 3, 4, 6, 9, 18
  4. 2,3,6,9,182, 3, 6, 9, 18
Explanation: This question tests 4th grade ability to find all factor pairs for whole numbers 1-100, recognize that a number is a multiple of each of its factors, determine if a number is a multiple of a given one-digit number, and determine whether a number is prime or composite (CCSS.4.OA.4). A factor is a whole number that divides another number evenly with no remainder—if a × b = n, then both a and b are factors of n, and (a, b) is a factor pair. To find all factor pairs, systematically check: does 1 divide n? does 2? does 3? and so on up to √n, stopping when factors start repeating. A prime number has exactly 2 factors (1 and itself), while a composite number has more than 2 factors. The number 1 is special—it's neither prime nor composite (only 1 factor). For the number 18, to find all factors: systematically check divisibility starting from 1 up to 18, listing all that divide evenly: 1,2,3,6,9,18. Choice A is correct because all factors are listed (checked all numbers 1 through 18) and none are missing or extra. This demonstrates systematic factor finding and understanding of prime/composite definitions. Choice B represents including non-factors, which happens when students include numbers that don't divide evenly. To help students: For finding factor pairs, use systematic approach—start with 1 (always works), check 2, 3, 4, 5, etc., stop when you start seeing the same pairs reversed. Example for 24: 1×24 ✓, 2×12 ✓, 3×8 ✓, 4×6 ✓, 5 doesn't work, 6×4 (already have 4×6, stop). For prime/composite, count factors: exactly 2 = prime, more than 2 = composite. Remember: 1 is neither (only 1 factor), 2 is only even prime. For multiples, divide: if no remainder, it IS a multiple (48 ÷ 6 = 8 R0 ✓). Use arrays to visualize: 12 objects can arrange as 1×12, 2×6, 3×4—each arrangement shows a factor pair. Connect: if f is a factor of n, then n is a multiple of f (inverse relationship). Watch for: missing factor pairs, including non-factors, calling 1 prime, thinking all odd numbers are prime (9, 15, 21 are composite), confusing factors with multiples, and not checking systematically.