How to find the factors of 52
Test every whole number from 1 up to the square root of 52 (√52 ≈ 7.211). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 52 ÷ 1 = 52 — so 1 and 52 are factors
- 52 ÷ 2 = 26 — so 2 and 26 are factors
- 52 ÷ 3 = 17.333 — not a whole number
- 52 ÷ 4 = 13 — so 4 and 13 are factors
- 52 ÷ 5 = 10.4 — not a whole number
- 52 ÷ 6 = 8.667 — not a whole number
- 52 ÷ 7 = 7.429 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 13, 26 and 52.
Prime factorization of 52
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 52 = 2² × 13. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) = 6.
Properties of 52
- 52 is a composite number.
- The sum of all its factors is 98; the sum of its proper factors (excluding 52) is 46, which makes it a deficient number (its proper factors add up to less than itself).
- 52 is not a perfect square, so its factors pair up evenly.
- Multiples of 52 include 104, 156, 208, 260 and so on.
Factors vs. multiples
Factors of 52 are the numbers that divide into it; multiples of 52 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 52?
The factors of 52 are 1, 2, 4, 13, 26 and 52. Each of these divides 52 with no remainder.
How many factors does 52 have?
52 has 6 positive factors, which form 3 factor pairs. Counting negative factors as well doubles that to 12.
What is the prime factorization of 52?
52 = 2² × 13. Its distinct prime factors are 2 and 13.
Is 52 a prime number?
No. 52 is composite because it has 6 factors, more than the two a prime number has.