The factors of 48 are the whole numbers that divide 48 exactly, leaving no remainder: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Use the calculator above for any number, or read on for the factor pairs, prime factorization and properties of 48.
What are the factors of 48?
A factor of 48 is any whole number that divides 48 with no remainder. Listing them from smallest to largest, the factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
So 48 is a composite number with 10 factors in total. Every number has 1 and itself as factors; the interesting work is finding the ones in between.
Factor pairs of 48
A factor pair is two numbers that multiply to give 48. The factor pairs of 48 are:
| Factor pair | Product |
|---|---|
| 1 × 48 | 48 |
| 2 × 24 | 48 |
| 3 × 16 | 48 |
| 4 × 12 | 48 |
| 6 × 8 | 48 |
Prime factorization of 48
The prime factorization breaks 48 down into a product of prime numbers only:
$$ 48 = 2^{4} \times 3 $$How to find the factors of 48, step by step
- Start at 1 — 1 divides every number, so 1 and 48 are always factors.
- Test each whole number from 2 upward: if it divides 48 exactly, it is a factor.
- Use factor pairs — each small factor gives a matching large factor, so you only need to test up to $\sqrt{48}$.
- List them in order to get all 10 factors of 48.
Factors versus multiples of 48
It is easy to mix these up. The factors of 48 are the numbers that divide into 48 (they are less than or equal to 48), while the multiples of 48 are what you get by multiplying 48 outward: 48, 96, 144, 192, and so on. In short: factors go in, multiples go out. 48 is an even number, and its smallest prime factor is 2.
Properties of 48
| Number of factors | 10 |
| Sum of factors | 124 |
| Sum of proper divisors | 76 |
| Prime or composite | Composite |
| Even or odd | Even |
| Perfect square | No |
| Prime factorization | 2^4 x 3 |
Is 48 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 48, those proper divisors add up to 76, which makes 48 an abundant number (its proper divisors sum to 76, which is more than 48). Most numbers are deficient; abundant and perfect numbers are comparatively rare, which is what makes this property interesting.
Using the factors of 48 for GCF and LCM
The prime factorization $2^{4} \times 3$ is the shortcut for combining 48 with another number. To find the greatest common factor (GCF), take the primes 48 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 50 Factors of 45 Factors of 44. 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.