Factors of 180

How to find the factors of 180

Test every whole number from 1 up to the square root of 180 (√180 ≈ 13.416). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 180 ÷ 1 = 180 — so 1 and 180 are factors
• 180 ÷ 2 = 90 — so 2 and 90 are factors
• 180 ÷ 3 = 60 — so 3 and 60 are factors
• 180 ÷ 4 = 45 — so 4 and 45 are factors
• 180 ÷ 5 = 36 — so 5 and 36 are factors
• 180 ÷ 6 = 30 — so 6 and 30 are factors
• 180 ÷ 7 = 25.714 — not a whole number
• 180 ÷ 8 = 22.5 — not a whole number
• 180 ÷ 9 = 20 — so 9 and 20 are factors
• 180 ÷ 10 = 18 — so 10 and 18 are factors
• 180 ÷ 11 = 16.364 — not a whole number
• 180 ÷ 12 = 15 — so 12 and 15 are factors
• 180 ÷ 13 = 13.846 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.

Prime factorization of 180

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

The primes you divided by give 180 = 2² × 3² × 5. From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) × (1 + 1) = 18.

Properties of 180

• 180 is a composite number.
• The sum of all its factors is 546; the sum of its proper factors (excluding 180) is 366, which makes it a abundant number (its proper factors add up to more than itself).
• 180 is not a perfect square, so its factors pair up evenly.
• Multiples of 180 include 360, 540, 720, 900 and so on.

Factors vs. multiples

Factors of 180 are the numbers that divide into it; multiples of 180 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.