Factors of 238

How to find the factors of 238

Test every whole number from 1 up to the square root of 238 (√238 ≈ 15.427). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 238 ÷ 1 = 238 — so 1 and 238 are factors
• 238 ÷ 2 = 119 — so 2 and 119 are factors
• 238 ÷ 3 = 79.333 — not a whole number
• 238 ÷ 4 = 59.5 — not a whole number
• 238 ÷ 5 = 47.6 — not a whole number
• 238 ÷ 6 = 39.667 — not a whole number
• 238 ÷ 7 = 34 — so 7 and 34 are factors
• 238 ÷ 8 = 29.75 — not a whole number
• 238 ÷ 9 = 26.444 — not a whole number
• 238 ÷ 10 = 23.8 — not a whole number
• 238 ÷ 11 = 21.636 — not a whole number
• 238 ÷ 12 = 19.833 — not a whole number
• 238 ÷ 13 = 18.308 — not a whole number
• 238 ÷ 14 = 17 — so 14 and 17 are factors
• 238 ÷ 15 = 15.867 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 7, 14, 17, 34, 119 and 238.

Prime factorization of 238

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

The primes you divided by give 238 = 2 × 7 × 17. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 238

• 238 is a composite number.
• The sum of all its factors is 432; the sum of its proper factors (excluding 238) is 194, which makes it a deficient number (its proper factors add up to less than itself).
• 238 is not a perfect square, so its factors pair up evenly.
• Multiples of 238 include 476, 714, 952, 1,190 and so on.

Factors vs. multiples

Factors of 238 are the numbers that divide into it; multiples of 238 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.