How to find the factors of 48
Test every whole number from 1 up to the square root of 48 (√48 ≈ 6.928). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 48 ÷ 1 = 48 — so 1 and 48 are factors
- 48 ÷ 2 = 24 — so 2 and 24 are factors
- 48 ÷ 3 = 16 — so 3 and 16 are factors
- 48 ÷ 4 = 12 — so 4 and 12 are factors
- 48 ÷ 5 = 9.6 — not a whole number
- 48 ÷ 6 = 8 — so 6 and 8 are factors
Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Prime factorization of 48
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 48 = 2⁴ × 3. From the exponents you can also count the factors without listing them: (4 + 1) × (1 + 1) = 10.
Properties of 48
- 48 is a composite number.
- The sum of all its factors is 124; the sum of its proper factors (excluding 48) is 76, which makes it a abundant number (its proper factors add up to more than itself).
- 48 is not a perfect square, so its factors pair up evenly.
- Multiples of 48 include 96, 144, 192, 240 and so on.
Factors vs. multiples
Factors of 48 are the numbers that divide into it; multiples of 48 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 48?
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. Each of these divides 48 with no remainder.
How many factors does 48 have?
48 has 10 positive factors, which form 5 factor pairs. Counting negative factors as well doubles that to 20.
What is the prime factorization of 48?
48 = 2⁴ × 3. Its distinct prime factors are 2 and 3.
Is 48 a prime number?
No. 48 is composite because it has 10 factors, more than the two a prime number has.