WorkedMathGlossary

Factors of 52

The factors of 52 are 1, 2, 4, 13, 26, 52. No, 52 is a composite number. Its prime factorization is 2^2 × 13.

Factors of 52
1, 2, 4, 13, 26, 52
6 factors
Prime or Composite
Composite
Perfect Square
No
Prime Factorization
2^2 × 13
Sum of Factors
98 (46 without 52 itself)

Factor pairs of 52

Every factor has a partner that multiplies with it to give 52. Listing pairs from the outside in is the fastest way to find all the factors: once the two numbers in a pair meet in the middle, you have them all.

PairCheck
1 and 521 × 52 = 52
2 and 262 × 26 = 52
4 and 134 × 13 = 52

Prime factorization of 52, step by step

Divide by the smallest prime that goes in evenly, then repeat on the result until you reach 1. The divisors you used are the prime factors.

StepDivideResult
152 ÷ 226
226 ÷ 213
313 ÷ 131

So 52 = 2 × 2 × 13, written compactly as 2^2 × 13.

Divisibility checks for 52

The quick rules a student uses before dividing, applied to 52:

Divisible byRuleFor 52Result
2last digit is evenlast digit 2yes
3digit sum divisible by 3digits add to 7no
4last two digits divisible by 452 ÷ 4yes
5last digit is 0 or 5last digit 2no
6divisible by both 2 and 3even, digit sum 7no
8last three digits divisible by 852 ÷ 8no
9digit sum divisible by 9digits add to 7no
10last digit is 0last digit 2no

Frequently Asked Questions

What are the factors of 52?

The factors of 52 are 1, 2, 4, 13, 26, 52.

Is 52 a prime number?

No, 52 is a composite number. Its prime factorization is 2^2 × 13.

How many factors does 52 have?

52 has 6 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^2 × 13 and multiply -- (2+1) × (1+1) = 6.

Is 52 even or odd?

52 is even (2 is one of its factors).

What is the sum of the factors of 52?

1 + 2 + 4 + 13 + 26 + 52 = 98. Leaving out 52 itself, the proper factors add to 46, less than 52, so 52 is a deficient number.

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