Factors of 352

How to find the factors of 352

Test every whole number from 1 up to the square root of 352 (√352 ≈ 18.762). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 352 ÷ 1 = 352 — so 1 and 352 are factors
• 352 ÷ 2 = 176 — so 2 and 176 are factors
• 352 ÷ 3 = 117.333 — not a whole number
• 352 ÷ 4 = 88 — so 4 and 88 are factors
• 352 ÷ 5 = 70.4 — not a whole number
• 352 ÷ 6 = 58.667 — not a whole number
• 352 ÷ 7 = 50.286 — not a whole number
• 352 ÷ 8 = 44 — so 8 and 44 are factors
• 352 ÷ 9 = 39.111 — not a whole number
• 352 ÷ 10 = 35.2 — not a whole number
• 352 ÷ 11 = 32 — so 11 and 32 are factors
• 352 ÷ 12 = 29.333 — not a whole number
• 352 ÷ 13 = 27.077 — not a whole number
• 352 ÷ 14 = 25.143 — not a whole number
• 352 ÷ 15 = 23.467 — not a whole number
• 352 ÷ 16 = 22 — so 16 and 22 are factors
• 352 ÷ 17 = 20.706 — not a whole number
• 352 ÷ 18 = 19.556 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176 and 352.

Prime factorization of 352

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

The primes you divided by give 352 = 2⁵ × 11. From the exponents you can also count the factors without listing them: (5 + 1) × (1 + 1) = 12.

Properties of 352

• 352 is a composite number.
• The sum of all its factors is 756; the sum of its proper factors (excluding 352) is 404, which makes it a abundant number (its proper factors add up to more than itself).
• 352 is not a perfect square, so its factors pair up evenly.
• Multiples of 352 include 704, 1,056, 1,408, 1,760 and so on.

Factors vs. multiples

Factors of 352 are the numbers that divide into it; multiples of 352 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.