Practice Unknown Factor Problems in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An unknown factor problem asks you to find a missing number in a multiplication equation, such as ?×6=48? \times 6 = 48 or 8×?=568 \times ? = 56.

If you know the total and one group size, division tells you how many groups — the missing factor is the answer to that division.

Showing a random 20 of 50 problems.

Example 1

challenge
Find both missing factors: ?×?=36? \times ? = 36 with the two factors equal.

Example 2

hard
A rectangle has area 60 and length 12. Find the width.

Example 3

challenge
For what whole numbers does ?×8=8×?? \times 8 = 8 \times ? hold true?

Example 4

medium
?×4=100? \times 4 = 100. Is the factor a whole number? Find it.

Example 5

easy
Check: is ?=9?=9 correct for ?×4=36? \times 4 = 36?

Example 6

medium
A number times 7 is 84. Find the number.

Example 7

medium
Solve: ?×9=108? \times 9 = 108.

Example 8

challenge
A teacher wants to split 72 markers among ?? groups so each group gets exactly 6 markers. Then she splits 72 differently into groups of ?? markers with 9 groups. Find both missing factors.

Example 9

medium
Solve: ?×12=144? \times 12 = 144.

Example 10

medium
A box of 12 pens costs \$36. How many boxes can you buy with \$108?

Example 11

easy
Solve: 3×?=213 \times ? = 21.

Example 12

medium
If 4×?=4×94 \times ? = 4 \times 9, what is ?? without multiplying?

Example 13

challenge
?×5=5×(3×4)? \times 5 = 5 \times (3 \times 4). Find ??.

Example 14

easy
1×?=121 \times ? = 12. Find ??.

Example 15

easy
Solve: ?×6=48? \times 6 = 48.

Example 16

easy
Solve: ?×3=24? \times 3 = 24.

Example 17

hard
Find ??: ?×?=49? \times ? = 49 where the two factors are equal whole numbers.

Example 18

medium
Maria has 84 stickers and gives the same number to each of her 7 friends with none left over. How many per friend? Write and solve.

Example 19

medium
Solve: ?×15=90? \times 15 = 90.

Example 20

challenge
Find two whole-number factors of 24 whose sum is 11.
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