calcfluent

Factors of 400

400 has 15 factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400. Its prime factorization is 2⁴ × 5².

Factor pairs of 400

Factor×FactorProduct
1×400400
2×200400
4×100400
5×80400
8×50400
10×40400
16×25400
20×20400

Negative pairs work too: (−1) × (−400), (−2) × (−200), … = 400.

Number of factors
15
Factor pairs
8
Sum of factors
961
Prime or composite
Composite
Even or odd
Even
Perfect square
Yes (20²)
Prime factorization 2⁴ × 5²

How to find the factors of 400

Test every whole number from 1 up to the square root of 400 (√400 ≈ 20.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 400 ÷ 1 = 400 — so 1 and 400 are factors
  • 400 ÷ 2 = 200 — so 2 and 200 are factors
  • 400 ÷ 3 = 133.333 — not a whole number
  • 400 ÷ 4 = 100 — so 4 and 100 are factors
  • 400 ÷ 5 = 80 — so 5 and 80 are factors
  • 400 ÷ 6 = 66.667 — not a whole number
  • 400 ÷ 7 = 57.143 — not a whole number
  • 400 ÷ 8 = 50 — so 8 and 50 are factors
  • 400 ÷ 9 = 44.444 — not a whole number
  • 400 ÷ 10 = 40 — so 10 and 40 are factors
  • 400 ÷ 11 = 36.364 — not a whole number
  • 400 ÷ 12 = 33.333 — not a whole number
  • 400 ÷ 13 = 30.769 — not a whole number
  • 400 ÷ 14 = 28.571 — not a whole number
  • 400 ÷ 15 = 26.667 — not a whole number
  • 400 ÷ 16 = 25 — so 16 and 25 are factors
  • 400 ÷ 17 = 23.529 — not a whole number
  • 400 ÷ 18 = 22.222 — not a whole number
  • 400 ÷ 19 = 21.053 — not a whole number
  • 400 ÷ 20 = 20 — so 20 and 20 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.

Prime factorization of 400

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

400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

The primes you divided by give 400 = 2⁴ × 5². From the exponents you can also count the factors without listing them: (4 + 1) × (2 + 1) = 15.

Properties of 400

  • 400 is a composite number.
  • The sum of all its factors is 961; the sum of its proper factors (excluding 400) is 561, which makes it a abundant number (its proper factors add up to more than itself).
  • 400 is a perfect square: 20 × 20. Perfect squares always have an odd number of factors.
  • Multiples of 400 include 800, 1,200, 1,600, 2,000 and so on.

Factors vs. multiples

Factors of 400 are the numbers that divide into it; multiples of 400 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 400?

The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400. Each of these divides 400 with no remainder.

How many factors does 400 have?

400 has 15 positive factors, which form 8 factor pairs. Counting negative factors as well doubles that to 30.

What is the prime factorization of 400?

400 = 2⁴ × 5². Its distinct prime factors are 2 and 5.

Is 400 a prime number?

No. 400 is composite because it has 15 factors, more than the two a prime number has.