Factor Calculator

Factors of 408

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, and 408. In total, 408 has 16 factors. Its prime factorization is 2³ × 3 × 17, and the sum of all its factors is 1080.

All factors of 408

Here are all 16 factors of 408, listed from smallest to largest.

123468121724345168102136204408

Factor pairs of 408

These 8 pairs of whole numbers each multiply to give 408.

1 × 408 = 408
2 × 204 = 408
3 × 136 = 408
4 × 102 = 408
6 × 68 = 408
8 × 51 = 408
12 × 34 = 408
17 × 24 = 408

Prime factorization of 408

Dividing 408 by the smallest prime at each step gives its prime factorization:

408 ÷ 2 = 204
204 ÷ 2 = 102
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
Result: 408 = 2 × 2 × 2 × 3 × 17 = 2³ × 3 × 17

The distinct prime factors of 408 are 2, 3, 17. To factorize any other number, use the prime factorization calculator.

Factor tree of 408

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

Factor tree of 40840822042102251317
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 408

Number of factors16
Sum of factors1080
Sum of proper factors672
Prime factorization2³ × 3 × 17
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 408 interesting

  • 408 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 8 different ways.
  • 408 is an abundant number: its proper factors sum to 672, which is 264 more than 408 itself.
  • 408 has 3 distinct prime factors (2, 3, 17), which is why it has so many divisors.

How to find the factors of 408 yourself

Divide 408 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 √408 ≈ 20.20, because every factor above that pairs with one below it.

408 ÷ 1 = 408 ✓
408 ÷ 2 = 204 ✓
408 ÷ 3 = 136 ✓
408 ÷ 4 = 102 ✓
408 ÷ 6 = 68 ✓
408 ÷ 8 = 51 ✓
408 ÷ 12 = 34 ✓
408 ÷ 17 = 24 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. The factor calculator does this automatically for any number.

Numbers mathematically connected to 408.

Frequently asked questions about 408

What are the factors of 408?

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, and 408. That is 16 factors in total, counting both 1 and 408.

Is 408 a prime number?

No, 408 is not prime — it is a composite number with 16 factors. A prime number has exactly two factors, but 408 is also divisible by 2.

What is the prime factorization of 408?

The prime factorization of 408 is 2³ × 3 × 17. Written out in full: 2 × 2 × 2 × 3 × 17 = 408. Its distinct prime factors are 2, 3, 17.

What two numbers multiply to give 408?

There are 8 pairs of whole numbers that multiply to 408: 1 × 408, 2 × 204, 3 × 136, 4 × 102, 6 × 68, 8 × 51, 12 × 34, 17 × 24.

What is the sum of the factors of 408?

Adding all the factors of 408 together gives 1080. Excluding 408 itself, the proper factors sum to 672.

Is 408 a perfect square?

No, 408 is not a perfect square. There is no whole number that multiplies by itself to give 408. The nearest perfect squares are 400 and 441.

What is the largest factor of 408 other than itself?

The largest factor of 408 apart from 408 itself is 204, since 408 ÷ 204 = 2.

How many factors does 408 have?

408 has 16 factors: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, and 408. You can verify this from the prime factorization 2³ × 3 × 17: add 1 to each exponent and multiply, giving 4 × 2 × 2 = 16.

Explore more

Try another number in the factor calculator, break 408 down further with the prime factorization calculator, or compare 408 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.