Factors of 225

How to find the factors of 225

Test every whole number from 1 up to the square root of 225 (√225 ≈ 15.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 225 ÷ 1 = 225 — so 1 and 225 are factors
• 225 ÷ 2 = 112.5 — not a whole number
• 225 ÷ 3 = 75 — so 3 and 75 are factors
• 225 ÷ 4 = 56.25 — not a whole number
• 225 ÷ 5 = 45 — so 5 and 45 are factors
• 225 ÷ 6 = 37.5 — not a whole number
• 225 ÷ 7 = 32.143 — not a whole number
• 225 ÷ 8 = 28.125 — not a whole number
• 225 ÷ 9 = 25 — so 9 and 25 are factors
• 225 ÷ 10 = 22.5 — not a whole number
• 225 ÷ 11 = 20.455 — not a whole number
• 225 ÷ 12 = 18.75 — not a whole number
• 225 ÷ 13 = 17.308 — not a whole number
• 225 ÷ 14 = 16.071 — not a whole number
• 225 ÷ 15 = 15 — so 15 and 15 are factors

Collecting both numbers from every successful division gives the complete list: 1, 3, 5, 9, 15, 25, 45, 75 and 225.

Prime factorization of 225

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

The primes you divided by give 225 = 3² × 5². From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) = 9.

Properties of 225

• 225 is a composite number.
• The sum of all its factors is 403; the sum of its proper factors (excluding 225) is 178, which makes it a deficient number (its proper factors add up to less than itself).
• 225 is a perfect square: 15 × 15. Perfect squares always have an odd number of factors.
• Multiples of 225 include 450, 675, 900, 1,125 and so on.

Factors vs. multiples

Factors of 225 are the numbers that divide into it; multiples of 225 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.