Factors of 90

How to find the factors of 90

Test every whole number from 1 up to the square root of 90 (√90 ≈ 9.487). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 90 ÷ 1 = 90 — so 1 and 90 are factors
• 90 ÷ 2 = 45 — so 2 and 45 are factors
• 90 ÷ 3 = 30 — so 3 and 30 are factors
• 90 ÷ 4 = 22.5 — not a whole number
• 90 ÷ 5 = 18 — so 5 and 18 are factors
• 90 ÷ 6 = 15 — so 6 and 15 are factors
• 90 ÷ 7 = 12.857 — not a whole number
• 90 ÷ 8 = 11.25 — not a whole number
• 90 ÷ 9 = 10 — so 9 and 10 are factors

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

Prime factorization of 90

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

The primes you divided by give 90 = 2 × 3² × 5. From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) × (1 + 1) = 12.

Properties of 90

• 90 is a composite number.
• The sum of all its factors is 234; the sum of its proper factors (excluding 90) is 144, which makes it a abundant number (its proper factors add up to more than itself).
• 90 is not a perfect square, so its factors pair up evenly.
• Multiples of 90 include 180, 270, 360, 450 and so on.

Factors vs. multiples

Factors of 90 are the numbers that divide into it; multiples of 90 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.