calcfluent

Factors of 450

450 has 18 factors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225 and 450. Its prime factorization is 2 × 3² × 5².

Factor pairs of 450

Factor×FactorProduct
1×450450
2×225450
3×150450
5×90450
6×75450
9×50450
10×45450
15×30450
18×25450

Negative pairs work too: (−1) × (−450), (−2) × (−225), … = 450.

Number of factors
18
Factor pairs
9
Sum of factors
1,209
Prime or composite
Composite
Even or odd
Even
Perfect square
No
Prime factorization 2 × 3² × 5²

How to find the factors of 450

Test every whole number from 1 up to the square root of 450 (√450 ≈ 21.213). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 450 ÷ 1 = 450 — so 1 and 450 are factors
  • 450 ÷ 2 = 225 — so 2 and 225 are factors
  • 450 ÷ 3 = 150 — so 3 and 150 are factors
  • 450 ÷ 4 = 112.5 — not a whole number
  • 450 ÷ 5 = 90 — so 5 and 90 are factors
  • 450 ÷ 6 = 75 — so 6 and 75 are factors
  • 450 ÷ 7 = 64.286 — not a whole number
  • 450 ÷ 8 = 56.25 — not a whole number
  • 450 ÷ 9 = 50 — so 9 and 50 are factors
  • 450 ÷ 10 = 45 — so 10 and 45 are factors
  • 450 ÷ 11 = 40.909 — not a whole number
  • 450 ÷ 12 = 37.5 — not a whole number
  • 450 ÷ 13 = 34.615 — not a whole number
  • 450 ÷ 14 = 32.143 — not a whole number
  • 450 ÷ 15 = 30 — so 15 and 30 are factors
  • 450 ÷ 16 = 28.125 — not a whole number
  • 450 ÷ 17 = 26.471 — not a whole number
  • 450 ÷ 18 = 25 — so 18 and 25 are factors
  • 450 ÷ 19 = 23.684 — not a whole number
  • 450 ÷ 20 = 22.5 — not a whole number
  • 450 ÷ 21 = 21.429 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225 and 450.

Prime factorization of 450

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

450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

The primes you divided by give 450 = 2 × 3² × 5². From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) × (2 + 1) = 18.

Properties of 450

  • 450 is a composite number.
  • The sum of all its factors is 1,209; the sum of its proper factors (excluding 450) is 759, which makes it a abundant number (its proper factors add up to more than itself).
  • 450 is not a perfect square, so its factors pair up evenly.
  • Multiples of 450 include 900, 1,350, 1,800, 2,250 and so on.

Factors vs. multiples

Factors of 450 are the numbers that divide into it; multiples of 450 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 450?

The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225 and 450. Each of these divides 450 with no remainder.

How many factors does 450 have?

450 has 18 positive factors, which form 9 factor pairs. Counting negative factors as well doubles that to 36.

What is the prime factorization of 450?

450 = 2 × 3² × 5². Its distinct prime factors are 2, 3 and 5.

Is 450 a prime number?

No. 450 is composite because it has 18 factors, more than the two a prime number has.