List Factors - Arithmetic Step by Step

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.

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.

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.

\mathrm{factors\ of}\ 36

Step 2 — Factor pair

Check the factor pair: 1 x 36 = 36.

\hl{1} \times \hl{36} = 36

Step 3 — Factor pair

Check the factor pair: 2 x 18 = 36.

\hl{2} \times \hl{18} = 36

Step 4 — Factor pair

Check the factor pair: 3 x 12 = 36.

\hl{3} \times \hl{12} = 36

Step 5 — Factor pair

Check the factor pair: 4 x 9 = 36.

\hl{4} \times \hl{9} = 36

Step 6 — Factor pair

Check the factor pair: 6 x 6 = 36.

\hl{6} \times \hl{6} = 36

Step 7 — Result

Read the final result.

\mathrm{factors:}\ \hl{1}, \hl{2}, \hl{3}, \hl{4}, \hl{6}, \hl{9}, \hl{12}, \hl{18}, \hl{36}