A girl planning how to arrange chairs for a school show

Find Factors and Identify Primes

Nadia must set up 12 chairs in equal rows for the school play. How many ways can she do it? Let's find out!

4th Grade Math

Step 1: Find a Factor Pair

This array shows 3 rows of 4, and 3 × 4 = 12. So 3 and 4 are a factor pair of 12. Which other pair makes 12 exactly?

2 × 6 = 12, so 2 and 6 are a factor pair. But 2 × 5 = 10 and 4 × 5 = 20, so those pairs do not make 12.

Step 2: Find All the Factors

Nadia lists every factor pair of 12: 1 × 12, 2 × 6, and 3 × 4. Now she wants one complete list of factors. Which list shows all the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6, and 12. And 12 is a multiple of every one of its factors!

Let's Remember

How to Find Factor Pairs

          Step 1: Start at 1 and test each number in order.

          Step 2: If it divides evenly, write its
          product partner.

          Step 3: Stop when the pairs start to repeat.

For 12: 1 × 12, 2 × 6, 3 × 4. After 3, the pairs flip and repeat.

Step 3: A Stubborn Number

Nadia tries 7 chairs. She tests rows of 2, 3, 4, 5, and 6. Every try leaves chairs sticking out! How many factor pairs does 7 have?

Only 1 × 7 = 7 works. A number with exactly two factors, 1 and itself, is called prime.

Prime or Composite?

The Rule

          Prime: exactly two factors, 1 and itself. Like 2, 3, 5, 7.

          Composite:
          more than two factors. Like 12.

          The number 1 is neither prime nor composite!

Watch Out!

          Odd does not always mean prime.
          The number 9 is odd, but 3 × 3 = 9, so 9 is composite!
        

Practice: Factor Pairs of 18

Test each number in order, starting at 1. Which list shows all the factor pairs of 18?

1 × 18 = 18, 2 × 9 = 18, and 3 × 6 = 18. 4 × 5 = 20, so that pair fails. And never forget the pair with 1!

Practice: Multiples

Is 56 a multiple of 7?

7 × 8 = 56, so 56 is a multiple of 7. That also means 7 and 8 are both factors of 56.

Word Problem

Jaylen plants 42 seeds in equal rows. He puts 6 seeds in each row, with none left over. How many rows does he plant?

6 × 7 = 42, so Jaylen plants 7 rows. 42 is a multiple of 6, so the rows come out even with no seeds left.

Prime or Composite?

Determine whether 29 is prime or composite. Test small factors: does 2, 3, 4, or 5 divide 29 evenly?

No number from 2 to 28 divides 29 evenly. Its only factors are 1 and 29, so 29 is prime.

Find the Missing Factor

7 × ? = 63

7 × 9 = 63, so the missing factor is 9. Check the others: 7 × 8 = 56 and 7 × 7 = 49.

Challenge: The Tricky 91

The number 91 looks prime, but looks can fool you. It is not even, and 9 + 1 = 10, so 3 fails too. Keep testing! Is 91 prime or composite?

7 × 13 = 91! Since 91 has the factors 1, 7, 13, and 91, it is composite. Always test 7 before you decide a number is prime.

Where could factor pairs help you in real life? Think about arranging chairs, splitting teams, or sharing snacks equally.

Great Work!

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factor multiple prime composite product determine