Factors of 900

How to find the factors of 900

Test every whole number from 1 up to the square root of 900 (√900 ≈ 30.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 900 ÷ 1 = 900 — so 1 and 900 are factors
• 900 ÷ 2 = 450 — so 2 and 450 are factors
• 900 ÷ 3 = 300 — so 3 and 300 are factors
• 900 ÷ 4 = 225 — so 4 and 225 are factors
• 900 ÷ 5 = 180 — so 5 and 180 are factors
• 900 ÷ 6 = 150 — so 6 and 150 are factors
• 900 ÷ 7 = 128.571 — not a whole number
• 900 ÷ 8 = 112.5 — not a whole number
• 900 ÷ 9 = 100 — so 9 and 100 are factors
• 900 ÷ 10 = 90 — so 10 and 90 are factors
• 900 ÷ 11 = 81.818 — not a whole number
• 900 ÷ 12 = 75 — so 12 and 75 are factors
• 900 ÷ 13 = 69.231 — not a whole number
• 900 ÷ 14 = 64.286 — not a whole number
• 900 ÷ 15 = 60 — so 15 and 60 are factors
• 900 ÷ 16 = 56.25 — not a whole number
• 900 ÷ 17 = 52.941 — not a whole number
• 900 ÷ 18 = 50 — so 18 and 50 are factors
• 900 ÷ 19 = 47.368 — not a whole number
• 900 ÷ 20 = 45 — so 20 and 45 are factors
• 900 ÷ 21 = 42.857 — not a whole number
• 900 ÷ 22 = 40.909 — not a whole number
• 900 ÷ 23 = 39.13 — not a whole number
• 900 ÷ 24 = 37.5 — not a whole number
• 900 ÷ 25 = 36 — so 25 and 36 are factors
• 900 ÷ 26 = 34.615 — not a whole number
• 900 ÷ 27 = 33.333 — not a whole number
• 900 ÷ 28 = 32.143 — not a whole number
• 900 ÷ 29 = 31.034 — not a whole number
• 900 ÷ 30 = 30 — so 30 and 30 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450 and 900.

Prime factorization of 900

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

The primes you divided by give 900 = 2² × 3² × 5². From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) × (2 + 1) = 27.

Properties of 900

• 900 is a composite number.
• The sum of all its factors is 2,821; the sum of its proper factors (excluding 900) is 1,921, which makes it a abundant number (its proper factors add up to more than itself).
• 900 is a perfect square: 30 × 30. Perfect squares always have an odd number of factors.
• Multiples of 900 include 1,800, 2,700, 3,600, 4,500 and so on.

Factors vs. multiples

Factors of 900 are the numbers that divide into it; multiples of 900 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.