Factor Calculator

Factors of 48

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. In total, 48 has 10 factors. Its prime factorization is 2⁴ × 3, and the sum of all its factors is 124.

All factors of 48

Here are all 10 factors of 48, listed from smallest to largest.

12346812162448

Factor pairs of 48

These 5 pairs of whole numbers each multiply to give 48.

1 × 48 = 48
2 × 24 = 48
3 × 16 = 48
4 × 12 = 48
6 × 8 = 48

Prime factorization of 48

Dividing 48 by the smallest prime at each step gives its prime factorization:

48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
Result: 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

The distinct prime factors of 48 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 48

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 48482242122623
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 48

Number of factors10
Sum of factors124
Sum of proper factors76
Prime factorization2⁴ × 3
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 48 interesting

  • 48 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
  • 48 is an abundant number: its proper factors sum to 76, which is 28 more than 48 itself.
  • 48 is a highly composite number — it has more factors (10) than any smaller positive integer. Numbers like this are useful in measurement systems because they divide evenly so many ways.

How to find the factors of 48 yourself

Divide 48 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √48 ≈ 6.93, because every factor above that pairs with one below it.

48 ÷ 1 = 48 ✓
48 ÷ 2 = 24 ✓
48 ÷ 3 = 16 ✓
48 ÷ 4 = 12 ✓
48 ÷ 6 = 8 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The factor calculator does this automatically for any number.

Numbers mathematically connected to 48.

Frequently asked questions about 48

What are the factors of 48?

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. That is 10 factors in total, counting both 1 and 48.

Is 48 a prime number?

No, 48 is not prime — it is a composite number with 10 factors. A prime number has exactly two factors, but 48 is also divisible by 2.

What is the prime factorization of 48?

The prime factorization of 48 is 2⁴ × 3. Written out in full: 2 × 2 × 2 × 2 × 3 = 48. Its distinct prime factors are 2, 3.

What two numbers multiply to give 48?

There are 5 pairs of whole numbers that multiply to 48: 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8.

What is the sum of the factors of 48?

Adding all the factors of 48 together gives 124. Excluding 48 itself, the proper factors sum to 76.

Is 48 a perfect square?

No, 48 is not a perfect square. There is no whole number that multiplies by itself to give 48. The nearest perfect squares are 36 and 49.

What is the largest factor of 48 other than itself?

The largest factor of 48 apart from 48 itself is 24, since 48 ÷ 24 = 2.

How many factors does 48 have?

48 has 10 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. You can verify this from the prime factorization 2⁴ × 3: add 1 to each exponent and multiply, giving 5 × 2 = 10.

Explore more

Try another number in the factor calculator, break 48 down further with the prime factorization calculator, or compare 48 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.