Factors of 208

How to find the factors of 208

Test every whole number from 1 up to the square root of 208 (√208 ≈ 14.422). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 208 ÷ 1 = 208 — so 1 and 208 are factors
• 208 ÷ 2 = 104 — so 2 and 104 are factors
• 208 ÷ 3 = 69.333 — not a whole number
• 208 ÷ 4 = 52 — so 4 and 52 are factors
• 208 ÷ 5 = 41.6 — not a whole number
• 208 ÷ 6 = 34.667 — not a whole number
• 208 ÷ 7 = 29.714 — not a whole number
• 208 ÷ 8 = 26 — so 8 and 26 are factors
• 208 ÷ 9 = 23.111 — not a whole number
• 208 ÷ 10 = 20.8 — not a whole number
• 208 ÷ 11 = 18.909 — not a whole number
• 208 ÷ 12 = 17.333 — not a whole number
• 208 ÷ 13 = 16 — so 13 and 16 are factors
• 208 ÷ 14 = 14.857 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 8, 13, 16, 26, 52, 104 and 208.

Prime factorization of 208

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

The primes you divided by give 208 = 2⁴ × 13. From the exponents you can also count the factors without listing them: (4 + 1) × (1 + 1) = 10.

Properties of 208

• 208 is a composite number.
• The sum of all its factors is 434; the sum of its proper factors (excluding 208) is 226, which makes it a abundant number (its proper factors add up to more than itself).
• 208 is not a perfect square, so its factors pair up evenly.
• Multiples of 208 include 416, 624, 832, 1,040 and so on.

Factors vs. multiples

Factors of 208 are the numbers that divide into it; multiples of 208 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.