Factor Calculator

Factors of 78

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78. In total, 78 has 8 factors. Its prime factorization is 2 × 3 × 13, and the sum of all its factors is 168.

All factors of 78

Here are all 8 factors of 78, listed from smallest to largest.

123613263978

Factor pairs of 78

These 4 pairs of whole numbers each multiply to give 78.

1 × 78 = 78
2 × 39 = 78
3 × 26 = 78
6 × 13 = 78

Prime factorization of 78

Dividing 78 by the smallest prime at each step gives its prime factorization:

78 ÷ 2 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
Result: 78 = 2 × 3 × 13 = 2 × 3 × 13

The distinct prime factors of 78 are 2, 3, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 78

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

Factor tree of 7878239313
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 78

Number of factors8
Sum of factors168
Sum of proper factors90
Prime factorization2 × 3 × 13
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 78 interesting

  • 78 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 78 is an abundant number: its proper factors sum to 90, which is 12 more than 78 itself.
  • 78 is a triangular number — it is the sum of the first 12 whole numbers (1 + 2 + … + 12 = 78).
  • 78 has 3 distinct prime factors (2, 3, 13), which is why it has so many divisors.

How to find the factors of 78 yourself

Divide 78 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 √78 ≈ 8.83, because every factor above that pairs with one below it.

78 ÷ 1 = 78 ✓
78 ÷ 2 = 39 ✓
78 ÷ 3 = 26 ✓
78 ÷ 6 = 13 ✓

Reading both columns gives every factor: 1, 2, 3, 6, 13, 26, 39, 78. The factor calculator does this automatically for any number.

Numbers mathematically connected to 78.

Frequently asked questions about 78

What are the factors of 78?

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78. That is 8 factors in total, counting both 1 and 78.

Is 78 a prime number?

No, 78 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 78 is also divisible by 2.

What is the prime factorization of 78?

The prime factorization of 78 is 2 × 3 × 13. Written out in full: 2 × 3 × 13 = 78. Its distinct prime factors are 2, 3, 13.

What two numbers multiply to give 78?

There are 4 pairs of whole numbers that multiply to 78: 1 × 78, 2 × 39, 3 × 26, 6 × 13.

What is the sum of the factors of 78?

Adding all the factors of 78 together gives 168. Excluding 78 itself, the proper factors sum to 90.

Is 78 a perfect square?

No, 78 is not a perfect square. There is no whole number that multiplies by itself to give 78. The nearest perfect squares are 64 and 81.

What is the largest factor of 78 other than itself?

The largest factor of 78 apart from 78 itself is 39, since 78 ÷ 39 = 2.

How many factors does 78 have?

78 has 8 factors: 1, 2, 3, 6, 13, 26, 39, and 78. You can verify this from the prime factorization 2 × 3 × 13: add 1 to each exponent and multiply, giving 2 × 2 × 2 = 8.

Explore more

Try another number in the factor calculator, break 78 down further with the prime factorization calculator, or compare 78 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.