Factors vs. multiples: how to explain the difference to a 4th grader

By 15Q20M Editorial · Last updated October 5, 2026

Factors fit into a number and multiples grow out of it. A factor divides the number evenly: the factors of 12 are 1, 2, 3, 4, 6, and 12. A multiple is the number times 1, 2, 3, and so on: 12, 24, 36, and the list never ends. Twelve is on both lists.

What is the difference between factors and multiples?

Both words come from the same multiplication fact. In 3 × 4 = 12, the 3 and the 4 are factors of 12, and 12 is a multiple of 3 and a multiple of 4. Factors are the pieces that multiply to make the number. Multiples are what you get when you multiply the number by 1, 2, 3, and so on. (Zero is technically a multiple of every number, since 12 × 0 = 0, but school lists, including our workbook's, start at the number times 1.)

That last row matters. A common shortcut says factors are smaller than the number and multiples are bigger. That is almost right, but 12 is both a factor of 12 and a multiple of 12, because 12 × 1 = 12. The "smaller, bigger" version makes it easy to leave the number itself off both lists, and our Grade 4 answer notes flag both slips.

How do you explain factors to a child with objects?

Use 24 small things that can sit in rows: LEGO bricks, coins, or crackers. Day 76, Question 5 of our Grade 4 workbook asks how many factor pairs 24 has. The answer is 4, and your child can find all of them by building rectangles. Read the left column out loud.

Each rectangle is a factor pair, and a number that leaves extra pieces, like 5, is not a factor. The rectangles also show the other word: 24 is a multiple of every number on the list, because each one goes into 24 a whole number of times.

How do you find all the factor pairs without missing one?

Go in order, starting at 1, and stop when the pairs start to repeat. For 24, test 1, 2, 3, 4, 5, 6. At 6 you get 6 × 4, which you already have as 4 × 6, so you are done. Writing the factors in a line shows the pairs nesting inside each other:

• 1 and 24 on the outside.
• 2 and 12 next.
• 3 and 8 next. Our answer notes flag this middle pair as easy to miss when factors are listed in a random order.
• 4 and 6 in the middle.

So the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Some numbers have a pair that is the same number twice. For 16, the pairs are 1 × 16, 2 × 8, and 4 × 4, so 16 has 5 factors, not 6: the 4 counts once. Day 76, Question 11 asks exactly this. Numbers like 4, 9, 16, 25, and 36 always have an odd number of factors for the same reason.

How do you explain prime and composite numbers?

Go back to the rectangles. Give your child 13 pieces and ask for every rectangle. There is only one: a single row of 13. A prime number has exactly two factors, 1 and itself, so it can only make one rectangle. A composite number has more than two factors, so it can make more than one. 12 can make three: 1 × 12, 2 × 6, and 3 × 4.

• 1 is neither prime nor composite. It has only one factor, itself (Day 77, Question 9).
• 2 is the only even prime (Day 77, Question 6). Every other even number has 2 as a factor, so it has more than two factors.
• Odd does not mean prime. 9, 15, and 21 are all odd, and all composite, because 3 goes into each of them. Day 77, Question 7 uses exactly those three as the wrong choices when it asks which number is prime. The answer is 13.

For numbers up to 100, there is a short test. If the number is 2, 3, 5, or 7, it is prime. Otherwise, try dividing by 2, 3, 5, and 7. If none of them goes in evenly, and the number is not 1, it is prime. This works because 10 × 10 = 100. A number up to 100 that is not prime (and not 1) splits into two factors that are both bigger than 1. Both cannot be bigger than 10, so one of them is between 2 and 10. That smaller factor is 2, 3, 5, or 7, or is built from them, like 4, 6, 8, 9, or 10. So if 2, 3, 5, and 7 all fail, no factor from 2 to 10 works either. The test catches the tricky ones: 91 looks prime, but 7 × 13 = 91, and 51 = 3 × 17.

What mistakes do kids make with factors and multiples?

Going in order, starting at 1, prevents the first two. For the next two, count the numbers in the list, and write a repeated middle factor like the 4 in 4 × 4 only once. The last two are about definitions, so say the definition out loud each time until it sticks.

When do kids learn factors, multiples, and prime numbers?

Children meet the word factor in 3rd grade, through multiplication and unknown-factor problems. Common Core makes factor pairs, multiples, and prime and composite numbers a formal topic in 4th grade, in one standard, 4.OA.B.4, for whole numbers from 1 to 100. Quick multiplication facts make it much easier, because finding factors is mostly running the times tables backward. In 6th grade, the same ideas come back as the greatest common factor and the least common multiple.

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