Find Factors and Identify Primes - 4th Grade Math

1. Identify all factor pairs of $36$.

   $(1,36)$, $(2,18)$, $(3,12)$, $(4,9)$, $(6,6)$. Find pairs that multiply to $36$.

2. What is a multiple of a whole number $d$?

   A number of the form $d \times k$ for a whole number $k$. Multiples are products of the number with any whole number.

3. Determine whether $72$ is a multiple of $8$.

   Yes, because $72 = 8 \times 9$. Check if $8$ divides $72$ evenly.

4. Find all factor pairs of $12$.

   $(1,12)$, $(2,6)$, $(3,4)$. Check pairs: $1 \times 12$, $2 \times 6$, $3 \times 4$.

5. Identify all factor pairs of $72$.

   $(1,72),(2,36),(3,24),(4,18),(6,12),(8,9)$. Check: $1×72$, $2×36$, $3×24$, $4×18$, $6×12$, $8×9=72$.

6. What does it mean if $a$ is a factor of $n$?

   $n$ is a multiple of $a$. If $a$ divides $n$ evenly, then $n$ is divisible by $a$.

7. What is the relationship between factors and multiples for numbers $a$ and $b$?

   If $a$ is a factor of $b$, then $b$ is a multiple of $a$. Factors and multiples have an inverse relationship.

8. Identify whether $97$ is prime or composite.

   Prime. Only divisible by $1$ and $97$, so it has exactly two factors.

9. Find all factor pairs of $24$.

   $(1,24)$, $(2,12)$, $(3,8)$, $(4,6)$. Check pairs: $1 \times 24$, $2 \times 12$, $3 \times 8$, $4 \times 6$.

10. Determine whether $56$ is a multiple of $7$.

    Yes, because $56 = 7 \times 8$. Divide $56 \div 7 = 8$, which is a whole number.

11. What is a factor of a whole number $n$?

    A whole number that divides $n$ with remainder $0$. A factor divides evenly into the number with no remainder.

12. What is a factor pair for a whole number $n$?

    Two whole numbers whose product is $n$. Factor pairs multiply together to give the original number.

13. Determine whether $97$ is prime or composite.

    Prime. $97$ has only factors $1$ and $97$.

14. Determine whether $91$ is prime or composite.

    Composite, because $91=7\times 13$. $91$ has factors beyond $1$ and itself: $7$ and $13$.

15. Identify whether $49$ is prime or composite.

    Composite. $49 = 7 \times 7$, so it has factors $1$, $7$, and $49$.

16. What factor pair is always true for any whole number $n$?

    $1$ and $n$ are always a factor pair of $n$. Every number divides itself and is divisible by $1$.

17. Which classification is correct for $1$: prime, composite, or neither?

    $1$ is neither prime nor composite. By definition, primes and composites must be greater than $1$.

18. Identify all factor pairs of $63$.

    $(1,63)$, $(3,21)$, $(7,9)$. Find pairs that multiply to $63$.

19. Determine whether $91$ is a multiple of $7$.

    Yes, because $91 = 7 \times 13$. Check if $7$ divides $91$ evenly.

20. Determine whether $49$ is prime or composite.

    Composite. $49 = 7 \times 7$, so it has more than two factors.

21. Determine whether $50$ is a multiple of $8$.

    No, because $8\times 6=48$ and $8\times 7=56$. $50$ falls between consecutive multiples of $8$.

22. What is the definition of a prime number in the range $1$ to $100$?

    A number with exactly two factors: $1$ and itself. Primes cannot be divided evenly by any other numbers.

23. Which number is neither prime nor composite?

    $1$. By definition, $1$ has only one factor (itself).

24. Determine whether $48$ is a multiple of $6$.

    Yes, because $48=6\times 8$. $48$ divided by $6$ equals $8$ with no remainder.

25. Identify all factor pairs of $56$.

    $(1,56)$, $(2,28)$, $(4,14)$, $(7,8)$. Find pairs that multiply to $56$.

26. What are all factors of $18$?

    $1,2,3,6,9,18$. Each number divides $18$ evenly: $18÷1=18$, $18÷2=9$, etc.

27. What are all factors of $20$?

    $1,2,4,5,10,20$. Each number divides $20$ evenly: $20÷1=20$, $20÷2=10$, etc.

28. What is the definition of a multiple of a whole number $k$?

    A number of the form $k \times m$ for a whole number $m$. Multiples are products of the number with whole numbers.

29. Find all factor pairs of $64$.

    $(1,64)$, $(2,32)$, $(4,16)$, $(8,8)$. Powers of $2$: $1 \times 64$, $2 \times 32$, $4 \times 16$, $8 \times 8$.

30. What is the definition of a factor of a whole number $n$?

    A whole number that divides $n$ with no remainder. A factor divides evenly into the number.

31. Find all factor pairs of $45$.

    $(1,45)$, $(3,15)$, $(5,9)$. Check pairs: $1 \times 45$, $3 \times 15$, $5 \times 9$.

32. Determine whether $49$ is a multiple of $7$.

    Yes, because $49=7\times 7$. $49$ divided by $7$ equals $7$ with no remainder.

33. Determine whether $70$ is a multiple of $8$.

    No, because $70$ is not $8 \times$ a whole number. $70 \div 8 = 8.75$, which is not a whole number.

34. Find all factor pairs of $36$.

    $(1,36)$, $(2,18)$, $(3,12)$, $(4,9)$, $(6,6)$. Check: $1 \times 36$, $2 \times 18$, $3 \times 12$, $4 \times 9$, $6 \times 6$.

35. Determine whether $81$ is a multiple of $3$.

    Yes, because $81 = 3 \times 27$. Check if $3$ divides $81$ evenly.

36. Identify whether $29$ is prime or composite.

    Prime. Only divisible by $1$ and $29$, so it has exactly two factors.

37. What is the correct classification of the number $1$: prime, composite, or neither?

    $1$ is neither prime nor composite. By definition, $1$ has only one factor: itself.

38. What is a prime number?

    A whole number $>1$ with exactly two factors: $1$ and itself. Prime numbers cannot be divided evenly by any other numbers.

39. Identify all factor pairs of $45$.

    $(1,45)$, $(3,15)$, $(5,9)$. Find pairs that multiply to $45$.

40. Determine whether $63$ is a multiple of $9$.

    Yes, because $63 = 9 \times 7$. Divide $63 \div 9 = 7$, which is a whole number.

41. Which numbers are the factors of $21$?

    $1$, $3$, $7$, $21$. Find all numbers that divide $21$ evenly.

42. Identify all factor pairs of $24$.

    $(1,24)$, $(2,12)$, $(3,8)$, $(4,6)$. Find pairs that multiply to $24$.

43. Determine whether $70$ is a multiple of $9$.

    No, because $70 \div 9$ is not a whole number. $70 \div 9 = 7.\overline{7}$, not a whole number.

44. What is the definition of a composite number in the range $1$ to $100$?

    A number with more than two factors. Composite numbers can be factored into smaller parts.

45. What is a composite number?

    A whole number $>1$ with more than two factors. Composite numbers can be factored into smaller whole numbers.

46. Find all factor pairs of $18$.

    $(1,18)$, $(2,9)$, $(3,6)$. Check pairs: $1 \times 18$, $2 \times 9$, $3 \times 6$.

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