Factors of 198

How to find the factors of 198

Test every whole number from 1 up to the square root of 198 (√198 ≈ 14.071). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 198 ÷ 1 = 198 — so 1 and 198 are factors
• 198 ÷ 2 = 99 — so 2 and 99 are factors
• 198 ÷ 3 = 66 — so 3 and 66 are factors
• 198 ÷ 4 = 49.5 — not a whole number
• 198 ÷ 5 = 39.6 — not a whole number
• 198 ÷ 6 = 33 — so 6 and 33 are factors
• 198 ÷ 7 = 28.286 — not a whole number
• 198 ÷ 8 = 24.75 — not a whole number
• 198 ÷ 9 = 22 — so 9 and 22 are factors
• 198 ÷ 10 = 19.8 — not a whole number
• 198 ÷ 11 = 18 — so 11 and 18 are factors
• 198 ÷ 12 = 16.5 — not a whole number
• 198 ÷ 13 = 15.231 — not a whole number
• 198 ÷ 14 = 14.143 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99 and 198.

Prime factorization of 198

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

The primes you divided by give 198 = 2 × 3² × 11. From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) × (1 + 1) = 12.

Properties of 198

• 198 is a composite number.
• The sum of all its factors is 468; the sum of its proper factors (excluding 198) is 270, which makes it a abundant number (its proper factors add up to more than itself).
• 198 is not a perfect square, so its factors pair up evenly.
• Multiples of 198 include 396, 594, 792, 990 and so on.

Factors vs. multiples

Factors of 198 are the numbers that divide into it; multiples of 198 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.