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Factors of 408

408 has 16 factors: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204 and 408. Its prime factorization is 2³ × 3 × 17.

Factor pairs of 408

Factor×FactorProduct
1×408408
2×204408
3×136408
4×102408
6×68408
8×51408
12×34408
17×24408

Negative pairs work too: (−1) × (−408), (−2) × (−204), … = 408.

Number of factors
16
Factor pairs
8
Sum of factors
1,080
Prime or composite
Composite
Even or odd
Even
Perfect square
No
Prime factorization 2³ × 3 × 17

How to find the factors of 408

Test every whole number from 1 up to the square root of 408 (√408 ≈ 20.199). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 408 ÷ 1 = 408 — so 1 and 408 are factors
  • 408 ÷ 2 = 204 — so 2 and 204 are factors
  • 408 ÷ 3 = 136 — so 3 and 136 are factors
  • 408 ÷ 4 = 102 — so 4 and 102 are factors
  • 408 ÷ 5 = 81.6 — not a whole number
  • 408 ÷ 6 = 68 — so 6 and 68 are factors
  • 408 ÷ 7 = 58.286 — not a whole number
  • 408 ÷ 8 = 51 — so 8 and 51 are factors
  • 408 ÷ 9 = 45.333 — not a whole number
  • 408 ÷ 10 = 40.8 — not a whole number
  • 408 ÷ 11 = 37.091 — not a whole number
  • 408 ÷ 12 = 34 — so 12 and 34 are factors
  • 408 ÷ 13 = 31.385 — not a whole number
  • 408 ÷ 14 = 29.143 — not a whole number
  • 408 ÷ 15 = 27.2 — not a whole number
  • 408 ÷ 16 = 25.5 — not a whole number
  • 408 ÷ 17 = 24 — so 17 and 24 are factors
  • 408 ÷ 18 = 22.667 — not a whole number
  • 408 ÷ 19 = 21.474 — not a whole number
  • 408 ÷ 20 = 20.4 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204 and 408.

Prime factorization of 408

Divide by the smallest prime that fits, and keep going until the quotient is 1:

408 ÷ 2 = 204
204 ÷ 2 = 102
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1

The primes you divided by give 408 = 2³ × 3 × 17. From the exponents you can also count the factors without listing them: (3 + 1) × (1 + 1) × (1 + 1) = 16.

Properties of 408

  • 408 is a composite number.
  • The sum of all its factors is 1,080; the sum of its proper factors (excluding 408) is 672, which makes it a abundant number (its proper factors add up to more than itself).
  • 408 is not a perfect square, so its factors pair up evenly.
  • Multiples of 408 include 816, 1,224, 1,632, 2,040 and so on.

Factors vs. multiples

Factors of 408 are the numbers that divide into it; multiples of 408 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 408?

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204 and 408. Each of these divides 408 with no remainder.

How many factors does 408 have?

408 has 16 positive factors, which form 8 factor pairs. Counting negative factors as well doubles that to 32.

What is the prime factorization of 408?

408 = 2³ × 3 × 17. Its distinct prime factors are 2, 3 and 17.

Is 408 a prime number?

No. 408 is composite because it has 16 factors, more than the two a prime number has.