Factors of 36

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. In total, 36 has 9 factors. Its prime factorization is 2² × 3², and the sum of all its factors is 91. 36 is also a perfect square, equal to 6 × 6.

All factors of 36

Here are all 9 factors of 36, listed from smallest to largest.

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Factor pairs of 36

These 5 pairs of whole numbers each multiply to give 36.

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

Notice the pair (6, 6) — because 36 is a perfect square, this pair uses the same number twice.

Prime factorization of 36

Dividing 36 by the smallest prime at each step gives its prime factorization:

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

Result: 36 = 2 × 2 × 3 × 3 = 2² × 3²

The distinct prime factors of 36 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 36

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 36

Number of factors	9
Sum of factors	91
Sum of proper factors	55
Prime factorization	2² × 3²
Prime or composite?	Composite
Even or odd?	Even
Perfect square?	Yes (6²)
Perfect cube?	No
Classification	Abundant

What makes 36 interesting

36 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
36 is a perfect square: 6 × 6 = 36. This is why it has an odd number of factors (9) — the pair (6, 6) counts only once.
36 is an abundant number: its proper factors sum to 55, which is 19 more than 36 itself.
36 is a highly composite number — it has more factors (9) than any smaller positive integer. Numbers like this are useful in measurement systems because they divide evenly so many ways.
36 is a triangular number — it is the sum of the first 8 whole numbers (1 + 2 + … + 8 = 36).

How to find the factors of 36 yourself

Divide 36 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √36 ≈ 6.00, because every factor above that pairs with one below it.

36 ÷ 1 = 36 ✓

36 ÷ 2 = 18 ✓

36 ÷ 3 = 12 ✓

36 ÷ 4 = 9 ✓

36 ÷ 6 = 6 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 9, 12, 18, 36. The factor calculator does this automatically for any number.

Numbers mathematically connected to 36.

Frequently asked questions about 36

What are the factors of 36?

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. That is 9 factors in total, counting both 1 and 36.

Is 36 a prime number?

No, 36 is not prime — it is a composite number with 9 factors. A prime number has exactly two factors, but 36 is also divisible by 2.

What is the prime factorization of 36?

The prime factorization of 36 is 2² × 3². Written out in full: 2 × 2 × 3 × 3 = 36. Its distinct prime factors are 2, 3.

What two numbers multiply to give 36?

There are 5 pairs of whole numbers that multiply to 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.

What is the sum of the factors of 36?

Adding all the factors of 36 together gives 91. Excluding 36 itself, the proper factors sum to 55.

Is 36 a perfect square?

Yes, 36 is a perfect square. It equals 6 × 6. Perfect squares always have an odd number of factors — 36 has 9.

What is the largest factor of 36 other than itself?

The largest factor of 36 apart from 36 itself is 18, since 36 ÷ 18 = 2.

How many factors does 36 have?

36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36. You can verify this from the prime factorization 2² × 3²: add 1 to each exponent and multiply, giving 3 × 3 = 9.

Explore more

Try another number in the factor calculator, break 36 down further with the prime factorization calculator, or compare 36 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.