How to find the factors of 36
Test every whole number from 1 up to the square root of 36 (√36 ≈ 6.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 36 ÷ 1 = 36 — so 1 and 36 are factors
- 36 ÷ 2 = 18 — so 2 and 18 are factors
- 36 ÷ 3 = 12 — so 3 and 12 are factors
- 36 ÷ 4 = 9 — so 4 and 9 are factors
- 36 ÷ 5 = 7.2 — not a whole number
- 36 ÷ 6 = 6 — so 6 and 6 are factors
Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Prime factorization of 36
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 36 = 2² × 3². From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) = 9.
Properties of 36
- 36 is a composite number.
- The sum of all its factors is 91; the sum of its proper factors (excluding 36) is 55, which makes it a abundant number (its proper factors add up to more than itself).
- 36 is a perfect square: 6 × 6. Perfect squares always have an odd number of factors.
- Multiples of 36 include 72, 108, 144, 180 and so on.
Factors vs. multiples
Factors of 36 are the numbers that divide into it; multiples of 36 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.
Frequently asked questions
What are the factors of 36?
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Each of these divides 36 with no remainder.
How many factors does 36 have?
36 has 9 positive factors, which form 5 factor pairs. Counting negative factors as well doubles that to 18.
What is the prime factorization of 36?
36 = 2² × 3². Its distinct prime factors are 2 and 3.
Is 36 a prime number?
No. 36 is composite because it has 9 factors, more than the two a prime number has.