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Factors of 462

462 has 16 factors: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231 and 462. Its prime factorization is 2 × 3 × 7 × 11.

Factor pairs of 462

Factor×FactorProduct
1×462462
2×231462
3×154462
6×77462
7×66462
11×42462
14×33462
21×22462

Negative pairs work too: (−1) × (−462), (−2) × (−231), … = 462.

Number of factors
16
Factor pairs
8
Sum of factors
1,152
Prime or composite
Composite
Even or odd
Even
Perfect square
No
Prime factorization 2 × 3 × 7 × 11

How to find the factors of 462

Test every whole number from 1 up to the square root of 462 (√462 ≈ 21.494). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 462 ÷ 1 = 462 — so 1 and 462 are factors
  • 462 ÷ 2 = 231 — so 2 and 231 are factors
  • 462 ÷ 3 = 154 — so 3 and 154 are factors
  • 462 ÷ 4 = 115.5 — not a whole number
  • 462 ÷ 5 = 92.4 — not a whole number
  • 462 ÷ 6 = 77 — so 6 and 77 are factors
  • 462 ÷ 7 = 66 — so 7 and 66 are factors
  • 462 ÷ 8 = 57.75 — not a whole number
  • 462 ÷ 9 = 51.333 — not a whole number
  • 462 ÷ 10 = 46.2 — not a whole number
  • 462 ÷ 11 = 42 — so 11 and 42 are factors
  • 462 ÷ 12 = 38.5 — not a whole number
  • 462 ÷ 13 = 35.538 — not a whole number
  • 462 ÷ 14 = 33 — so 14 and 33 are factors
  • 462 ÷ 15 = 30.8 — not a whole number
  • 462 ÷ 16 = 28.875 — not a whole number
  • 462 ÷ 17 = 27.176 — not a whole number
  • 462 ÷ 18 = 25.667 — not a whole number
  • 462 ÷ 19 = 24.316 — not a whole number
  • 462 ÷ 20 = 23.1 — not a whole number
  • 462 ÷ 21 = 22 — so 21 and 22 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231 and 462.

Prime factorization of 462

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

462 ÷ 2 = 231
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1

The primes you divided by give 462 = 2 × 3 × 7 × 11. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 16.

Properties of 462

  • 462 is a composite number.
  • The sum of all its factors is 1,152; the sum of its proper factors (excluding 462) is 690, which makes it a abundant number (its proper factors add up to more than itself).
  • 462 is not a perfect square, so its factors pair up evenly.
  • Multiples of 462 include 924, 1,386, 1,848, 2,310 and so on.

Factors vs. multiples

Factors of 462 are the numbers that divide into it; multiples of 462 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 462?

The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231 and 462. Each of these divides 462 with no remainder.

How many factors does 462 have?

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

What is the prime factorization of 462?

462 = 2 × 3 × 7 × 11. Its distinct prime factors are 2, 3, 7 and 11.

Is 462 a prime number?

No. 462 is composite because it has 16 factors, more than the two a prime number has.