Factors of 209

How to find the factors of 209

Test every whole number from 1 up to the square root of 209 (√209 ≈ 14.457). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 209 ÷ 1 = 209 — so 1 and 209 are factors
• 209 ÷ 2 = 104.5 — not a whole number
• 209 ÷ 3 = 69.667 — not a whole number
• 209 ÷ 4 = 52.25 — not a whole number
• 209 ÷ 5 = 41.8 — not a whole number
• 209 ÷ 6 = 34.833 — not a whole number
• 209 ÷ 7 = 29.857 — not a whole number
• 209 ÷ 8 = 26.125 — not a whole number
• 209 ÷ 9 = 23.222 — not a whole number
• 209 ÷ 10 = 20.9 — not a whole number
• 209 ÷ 11 = 19 — so 11 and 19 are factors
• 209 ÷ 12 = 17.417 — not a whole number
• 209 ÷ 13 = 16.077 — not a whole number
• 209 ÷ 14 = 14.929 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 11, 19 and 209.

Prime factorization of 209

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

The primes you divided by give 209 = 11 × 19. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 209

• 209 is a composite number.
• The sum of all its factors is 240; the sum of its proper factors (excluding 209) is 31, which makes it a deficient number (its proper factors add up to less than itself).
• 209 is not a perfect square, so its factors pair up evenly.
• Multiples of 209 include 418, 627, 836, 1,045 and so on.

Factors vs. multiples

Factors of 209 are the numbers that divide into it; multiples of 209 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.