The factors of 52 are the whole numbers that divide 52 exactly, leaving no remainder: 1, 2, 4, 13, 26, 52. Use the calculator above for any number, or read on for the factor pairs, prime factorization and properties of 52.
What are the factors of 52?
A factor of 52 is any whole number that divides 52 with no remainder. Listing them from smallest to largest, the factors of 52 are:
1, 2, 4, 13, 26, 52
So 52 is a composite number with 6 factors in total. Every number has 1 and itself as factors; the interesting work is finding the ones in between.
Factor pairs of 52
A factor pair is two numbers that multiply to give 52. The factor pairs of 52 are:
| Factor pair | Product |
|---|---|
| 1 × 52 | 52 |
| 2 × 26 | 52 |
| 4 × 13 | 52 |
Prime factorization of 52
The prime factorization breaks 52 down into a product of prime numbers only:
$$ 52 = 2^{2} \times 13 $$How to find the factors of 52, step by step
- Start at 1 — 1 divides every number, so 1 and 52 are always factors.
- Test each whole number from 2 upward: if it divides 52 exactly, it is a factor.
- Use factor pairs — each small factor gives a matching large factor, so you only need to test up to $\sqrt{52}$.
- List them in order to get all 6 factors of 52.
Factors versus multiples of 52
It is easy to mix these up. The factors of 52 are the numbers that divide into 52 (they are less than or equal to 52), while the multiples of 52 are what you get by multiplying 52 outward: 52, 104, 156, 208, and so on. In short: factors go in, multiples go out. 52 is an even number, and its smallest prime factor is 2.
Properties of 52
| Number of factors | 6 |
| Sum of factors | 98 |
| Sum of proper divisors | 46 |
| Prime or composite | Composite |
| Even or odd | Even |
| Perfect square | No |
| Prime factorization | 2^2 x 13 |
Is 52 abundant, deficient or perfect?
Number theorists classify a number by comparing it to the sum of its proper divisors (all its factors except itself). For 52, those proper divisors add up to 46, which makes 52 a deficient number (its proper divisors sum to 46, which is less than 52). Most numbers are deficient; abundant and perfect numbers are comparatively rare, which is what makes this property interesting.
Using the factors of 52 for GCF and LCM
The prime factorization $2^{2} \times 13$ is the shortcut for combining 52 with another number. To find the greatest common factor (GCF), take the primes 52 shares with the other number, each to the lowest power. For the least common multiple (LCM), take every prime that appears in either number, each to the highest power. This is why the prime factorization is worth writing down — it does the heavy lifting for fractions, ratios and simplification.
Related factors and tools
Explore more: Factors of 54 Factors of 50 Factors of 48. Or find the factors of any number with the Factor Calculator. Exponents are the reverse idea — see logarithms and read the formal reference on divisors at Wikipedia.