Finding factors and multiples up to 100
In 4th grade, children learn to find every factor pair of a number up to 100, to see that it is a multiple of each factor, and to spot multiples of one-digit numbers.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 4th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
4 × 9 = 36. Which sentence is true?
- 4 is a multiple of 36.
- 36 is a multiple of 4, but not of 9.
- 36 is a multiple of both 4 and 9.
Why this matters
Knowing how a number breaks into factors gives your child a real feel for how numbers are built. This year it helps them see why 2/3 and 8/12 are equal: multiply 2 and 3 by the same factor, 4, and you get 8 and 12. Next year, finding a common denominator for 1/4 and 1/6 means finding a shared multiple, 12. And at home, factors are how you share snacks evenly or set out chairs in equal rows.
Next comes spotting prime numbers, where your child uses factor pairs to sort numbers into two kinds.
Where kids can get stuck
- Missing factor pairs, such as finding 2 × 18 and 3 × 12 for 36 but not 4 × 9 or 6 × 6.
- Mixing up factors and multiples, saying 12 is a factor of 3 when they mean it is a multiple of 3.
- Leaving out 1 and the number itself, so the factors of 15 are listed as only 3 and 5.
How you can help
- Arrange crackers or blocks into rectangles on the kitchen table. Ask your child how many different rectangles they can make with 18, and say the factor pair for each one: 1 × 18, 2 × 9, and 3 × 6.
- Ask a sharing question at snack time: "Could we share these 20 grapes equally among 3 people? Among 4?" Connect each yes to a factor of 20 and each no to a number that is not.
- Skip count by 7s in the car, or by any number from 2 to 9. Then name a number under 100 and ask if you would land on it. 63 is a multiple of 7, since 7 × 9 = 63, but 65 is not.
Want a little more? Try Bobby's Math Club for free practice that adapts to your child.
Questions parents ask
Why is my child learning factors with rectangles and tiles?
Rectangles make factors easy to see. If 12 tiles can be arranged as 3 rows of 4, then 3 and 4 are factors of 12, and 12 is a multiple of both. Every different rectangle is another factor pair: 1 × 12, 2 × 6, and 3 × 4. The picture helps the words factor and multiple make sense, instead of being definitions to memorize.
How does my child know when they have found all the factor pairs?
A good method is to test numbers in order, starting at 1: does 1 work, does 2 work, does 3 work, and so on. Once the pairs start repeating in reverse, all of them have been found. For 36, the pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6. The next number that works is 9, which is already in a pair, so the list is complete.
What is the difference between a factor and a multiple?
Factors are the numbers that multiply to make a number, so the factors of 12 are 1, 2, 3, 4, 6, and 12. Multiples are what you get by counting by a number: 12, 24, 36, and on and on. The two are linked, since 12 is a multiple of every one of its factors. One way to remember it: a number has only a few factors, but its multiples never end.
Make learning math fun
Bobby's Math Club turns 4th grade math practice into something fun to do together.
- Free, unlimited practice for every child in your family
- Practice that starts where your child is and grows with them
- Hints when they are stuck, and a celebration when it clicks
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 4.OA.B.4: “Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.OA.4)