Factors and Multiples

List Factors

Find all factors of 36 by testing every whole number from 1 to 36. When a number divides 36 evenly, both that number and its partner are factors. Recording factor pairs keeps the list organized and complete.

Example

List factor pairs of 36 and collect the ordered factors.

highlighted = computed this step

Step 1 — Set up

Set up the numbers to test.

factors of 36\mathrm{factors\ of}\ 36
Find factor pairs that multiply to 36.target product: 36pair 1not yetpair 2not yetpair 3not yetpair 4not yetpair 5not yetcollected factorsstart with an empty list5 pairs, 9 factors

Step 2 — Factor pair

Check the factor pair: 1 x 36 = 36.

1×36=36\hl{1} \times \hl{36} = 36
Pair 1: 1 x 36 = 36.target product: 36pair 11 x 36= 36pair 2not yetpair 3not yetpair 4not yetpair 5not yetcollected factors1365 pairs, 9 factors

Step 3 — Factor pair

Check the factor pair: 2 x 18 = 36.

2×18=36\hl{2} \times \hl{18} = 36
Pair 2: 2 x 18 = 36.target product: 36pair 11 x 36= 36pair 22 x 18= 36pair 3not yetpair 4not yetpair 5not yetcollected factors1218365 pairs, 9 factors

Step 4 — Factor pair

Check the factor pair: 3 x 12 = 36.

3×12=36\hl{3} \times \hl{12} = 36
Pair 3: 3 x 12 = 36.target product: 36pair 11 x 36= 36pair 22 x 18= 36pair 33 x 12= 36pair 4not yetpair 5not yetcollected factors1231218365 pairs, 9 factors

Step 5 — Factor pair

Check the factor pair: 4 x 9 = 36.

4×9=36\hl{4} \times \hl{9} = 36
Pair 4: 4 x 9 = 36.target product: 36pair 11 x 36= 36pair 22 x 18= 36pair 33 x 12= 36pair 44 x 9= 36pair 5not yetcollected factors123491218365 pairs, 9 factors

Step 6 — Factor pair

Check the factor pair: 6 x 6 = 36.

6×6=36\hl{6} \times \hl{6} = 36
Pair 5: 6 x 6 = 36.target product: 36pair 11 x 36= 36pair 22 x 18= 36pair 33 x 12= 36pair 44 x 9= 36pair 56 x 6= 36collected factors1234691218365 pairs, 9 factors

Step 7 — Result

Read the final result.

factors: 1,2,3,4,6,9,12,18,36\mathrm{factors:}\ \hl{1}, \hl{2}, \hl{3}, \hl{4}, \hl{6}, \hl{9}, \hl{12}, \hl{18}, \hl{36}
Collect the factors in order: 1, 2, 3, 4, 6, 9, 12, 18, 36.target product: 36pair 11 x 36= 36pair 22 x 18= 36pair 33 x 12= 36pair 44 x 9= 36pair 56 x 6= 36collected factors1234691218365 pairs, 9 factors
factor-pairs Every factor of a number comes with a partner. For example, because 3 × 12 = 36, both 3 and 12 are factors of 36. Testing pairs (1 and 36, 2 and 18, …) means you only need to check up to the square root.