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Factors of 402

402 has 8 factors: 1, 2, 3, 6, 67, 134, 201 and 402. Its prime factorization is 2 × 3 × 67.

Factor pairs of 402

Factor×FactorProduct
1×402402
2×201402
3×134402
6×67402

Negative pairs work too: (−1) × (−402), (−2) × (−201), … = 402.

Number of factors
8
Factor pairs
4
Sum of factors
816
Prime or composite
Composite
Even or odd
Even
Perfect square
No
Prime factorization 2 × 3 × 67

How to find the factors of 402

Test every whole number from 1 up to the square root of 402 (√402 ≈ 20.050). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 402 ÷ 1 = 402 — so 1 and 402 are factors
  • 402 ÷ 2 = 201 — so 2 and 201 are factors
  • 402 ÷ 3 = 134 — so 3 and 134 are factors
  • 402 ÷ 4 = 100.5 — not a whole number
  • 402 ÷ 5 = 80.4 — not a whole number
  • 402 ÷ 6 = 67 — so 6 and 67 are factors
  • 402 ÷ 7 = 57.429 — not a whole number
  • 402 ÷ 8 = 50.25 — not a whole number
  • 402 ÷ 9 = 44.667 — not a whole number
  • 402 ÷ 10 = 40.2 — not a whole number
  • 402 ÷ 11 = 36.545 — not a whole number
  • 402 ÷ 12 = 33.5 — not a whole number
  • 402 ÷ 13 = 30.923 — not a whole number
  • 402 ÷ 14 = 28.714 — not a whole number
  • 402 ÷ 15 = 26.8 — not a whole number
  • 402 ÷ 16 = 25.125 — not a whole number
  • 402 ÷ 17 = 23.647 — not a whole number
  • 402 ÷ 18 = 22.333 — not a whole number
  • 402 ÷ 19 = 21.158 — not a whole number
  • 402 ÷ 20 = 20.1 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 67, 134, 201 and 402.

Prime factorization of 402

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

402 ÷ 2 = 201
201 ÷ 3 = 67
67 ÷ 67 = 1

The primes you divided by give 402 = 2 × 3 × 67. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 402

  • 402 is a composite number.
  • The sum of all its factors is 816; the sum of its proper factors (excluding 402) is 414, which makes it a abundant number (its proper factors add up to more than itself).
  • 402 is not a perfect square, so its factors pair up evenly.
  • Multiples of 402 include 804, 1,206, 1,608, 2,010 and so on.

Factors vs. multiples

Factors of 402 are the numbers that divide into it; multiples of 402 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 402?

The factors of 402 are 1, 2, 3, 6, 67, 134, 201 and 402. Each of these divides 402 with no remainder.

How many factors does 402 have?

402 has 8 positive factors, which form 4 factor pairs. Counting negative factors as well doubles that to 16.

What is the prime factorization of 402?

402 = 2 × 3 × 67. Its distinct prime factors are 2, 3 and 67.

Is 402 a prime number?

No. 402 is composite because it has 8 factors, more than the two a prime number has.