1,2,3,4,6,9,12,18,36

The square root of 36 rounded up to the nearest integer is 6. This is the limit to test our divisions because any number greater than 6 times 6 is greater than 36. So, we stop at 6.

Let's test the values 1 through 6 for division into 36.

• 36/1 = 36. Remainder = 0. So, 36 and 1 are factors.
• 36/2 = 18. Remainder = 0. So, 18 and 2 are factors.
• 36/3 = 12. Remainder = 0. So, 12 and 3 are factors.
• 36/4 = 9. Remainder = 0. So, 9 and 4 are factors.
• 36/5 = 7. Remainder = 1. So, 7 isn't a factor.
• 36/6 = 6. Remainder = 0. So, 6 and 6 are factors.

Factors of a number 'x' are numbers that can divide 'x' without remainder, ie, remainder = 0. So, choosing only the numbers that meet this criteria from the list above, we find that the numbers which divide 36 (including 36) with no remainder are: 36, 18, 12, 9, 6, 4, 3, 2, 1.

So, the factors of the number 36 are: 36, 18, 12, 9, 6, 4, 3, 2, 1.

A composite number has more than two factors. A prime number has only two factors: 1 and itself. The number 1 is neither prime nor composite.

Because the number 36 has 9 factors, it is termed a composite number in mathematics.