Factors of 210

How to find the factors of 210

Test every whole number from 1 up to the square root of 210 (√210 ≈ 14.491). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 210 ÷ 1 = 210 — so 1 and 210 are factors
• 210 ÷ 2 = 105 — so 2 and 105 are factors
• 210 ÷ 3 = 70 — so 3 and 70 are factors
• 210 ÷ 4 = 52.5 — not a whole number
• 210 ÷ 5 = 42 — so 5 and 42 are factors
• 210 ÷ 6 = 35 — so 6 and 35 are factors
• 210 ÷ 7 = 30 — so 7 and 30 are factors
• 210 ÷ 8 = 26.25 — not a whole number
• 210 ÷ 9 = 23.333 — not a whole number
• 210 ÷ 10 = 21 — so 10 and 21 are factors
• 210 ÷ 11 = 19.091 — not a whole number
• 210 ÷ 12 = 17.5 — not a whole number
• 210 ÷ 13 = 16.154 — not a whole number
• 210 ÷ 14 = 15 — so 14 and 15 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105 and 210.

Prime factorization of 210

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

The primes you divided by give 210 = 2 × 3 × 5 × 7. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 16.

Properties of 210

• 210 is a composite number.
• The sum of all its factors is 576; the sum of its proper factors (excluding 210) is 366, which makes it a abundant number (its proper factors add up to more than itself).
• 210 is not a perfect square, so its factors pair up evenly.
• Multiples of 210 include 420, 630, 840, 1,050 and so on.

Factors vs. multiples

Factors of 210 are the numbers that divide into it; multiples of 210 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.