Factors of 242

How to find the factors of 242

Test every whole number from 1 up to the square root of 242 (√242 ≈ 15.556). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 242 ÷ 1 = 242 — so 1 and 242 are factors
• 242 ÷ 2 = 121 — so 2 and 121 are factors
• 242 ÷ 3 = 80.667 — not a whole number
• 242 ÷ 4 = 60.5 — not a whole number
• 242 ÷ 5 = 48.4 — not a whole number
• 242 ÷ 6 = 40.333 — not a whole number
• 242 ÷ 7 = 34.571 — not a whole number
• 242 ÷ 8 = 30.25 — not a whole number
• 242 ÷ 9 = 26.889 — not a whole number
• 242 ÷ 10 = 24.2 — not a whole number
• 242 ÷ 11 = 22 — so 11 and 22 are factors
• 242 ÷ 12 = 20.167 — not a whole number
• 242 ÷ 13 = 18.615 — not a whole number
• 242 ÷ 14 = 17.286 — not a whole number
• 242 ÷ 15 = 16.133 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 11, 22, 121 and 242.

Prime factorization of 242

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

The primes you divided by give 242 = 2 × 11². From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) = 6.

Properties of 242

• 242 is a composite number.
• The sum of all its factors is 399; the sum of its proper factors (excluding 242) is 157, which makes it a deficient number (its proper factors add up to less than itself).
• 242 is not a perfect square, so its factors pair up evenly.
• Multiples of 242 include 484, 726, 968, 1,210 and so on.

Factors vs. multiples

Factors of 242 are the numbers that divide into it; multiples of 242 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.