GOZUNTA
Try it now
All courses Math Foundations · MF.NS.5 5 of 60
Find factors, multiples, common factors, and common multiples to solve numerical and contextual problems.

List all factors of a number

Problem
List all positive factors of 36 in order from least to greatest. Give only the complete factor list.
Your answer
With a free account

Turn browsing into a plan.

Pick an objective, make a session, and give your practice a clear beginning and end.

Create a free account
With paid access

Open the complete course.

A subscription unlocks every problem type and variant in your selected course, not only the starter set.

Compare plans

Hint

Begin by finding factor pairs of 36, starting with 1 × 36. Then test the next whole numbers to see which ones divide 36 evenly.

Factors come in multiplication pairs whose product is 36. Be sure to record both numbers in each pair and stop when the pairs start repeating.

Solution walkthrough

01

Start with the smallest divisors

\[1~×~36~=~36,~2~×~18~=~36,~3~×~12~=~36\]

A factor pair is two whole numbers whose product is 36. Starting at 1 helps make sure no positive factors are missed.

02

Keep going until the pairs meet

\[4~×~9~=~36,~6~×~6~=~36\]

These are the remaining factor pairs. After 6 × 6, the pairs would just repeat in reverse order, so the full set has been found.

03

Collect every factor once

\[\text{Factor}~\text{pairs}:~(1,~36),~(2,~18),~(3,~12),~(4,~9),~(6,~6)\]

Take both numbers from each pair, but include 6 only once because 6 × 6 uses the same factor twice.

04

Write the factors from least to greatest

\[1,~2,~3,~4,~6,~9,~12,~18,~36\]

This is the complete ordered list of all positive factors of 36.

+

Another way

  1. You can check the list by dividing 36 by each number: 36 ÷ 1, 36 ÷ 2, 36 ÷ 3, 36 ÷ 4, 36 ÷ 6, 36 ÷ 9, 36 ÷ 12, 36 ÷ 18, and 36 ÷ 36 all give whole numbers.

!

Common mistake

A common mistake is to stop after the small divisors and write 1, 2, 3, 4, 6. Those are only half of the factors. Each small factor has a matching partner, so 9, 12, 18, and 36 must also be included.