Factors of 36
- Input
- 36
- Expected output
- 1, 2, 3, 4, 6, 9, 12, 18, 36
Nine factors, sum 91, perfect square.
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factors of 36
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36: nine numbers that divide 36 with no remainder. The calculator above opens with 36 already filled in and shows the factorization, the pairs of factors and the sum of the factors, which is 91.
Nine factors, sum 91, perfect square.
Six factors, sum 28.
Eight factors, 24 = 2³ × 3.
Eight factors, 30 = 2 × 3 × 5.
Twelve factors, 60 = 2² × 3 × 5.
There are two ways. The direct one is to test the whole numbers from 1 up to the square root of the number: each time the division is exact you gain two divisors, the tested one and the quotient. For 36, testing 1, 2, 3, 4, 5 and 6 gives the pairs (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6). Factoring is faster for large numbers: break the number into primes and combine the powers, which is what the Step by step tab shows.
They are 1, 2, 3, 4, 6, 9, 12, 18 and 36. The pairs that multiply to 36 are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.
Nine. With 36 = 2² × 3², the count is (2 + 1) × (2 + 1) = 9. Perfect squares always have an odd number of factors.
No. A prime has only two factors, 1 and itself, and 36 has nine. It is a composite number, and also abundant, since its proper factors add up to 55.
In school arithmetic, only the positive ones. In algebra each factor also counts with a negative sign, and then the list has 18 numbers, from -36 to 36 without zero.
36 has 9 divisors
The proper divisors add up to 55, which is 19 more than 36: an abundant number.
Divisors that are prime are highlighted.
Accepts whole numbers of up to 18 digits. Everything runs in your browser with exact arithmetic.
Related: GCD and LCM · Prime numbers · Simplify fractions