Factors of 355

How to find the factors of 355

Test every whole number from 1 up to the square root of 355 (√355 ≈ 18.841). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 355 ÷ 1 = 355 — so 1 and 355 are factors
• 355 ÷ 2 = 177.5 — not a whole number
• 355 ÷ 3 = 118.333 — not a whole number
• 355 ÷ 4 = 88.75 — not a whole number
• 355 ÷ 5 = 71 — so 5 and 71 are factors
• 355 ÷ 6 = 59.167 — not a whole number
• 355 ÷ 7 = 50.714 — not a whole number
• 355 ÷ 8 = 44.375 — not a whole number
• 355 ÷ 9 = 39.444 — not a whole number
• 355 ÷ 10 = 35.5 — not a whole number
• 355 ÷ 11 = 32.273 — not a whole number
• 355 ÷ 12 = 29.583 — not a whole number
• 355 ÷ 13 = 27.308 — not a whole number
• 355 ÷ 14 = 25.357 — not a whole number
• 355 ÷ 15 = 23.667 — not a whole number
• 355 ÷ 16 = 22.188 — not a whole number
• 355 ÷ 17 = 20.882 — not a whole number
• 355 ÷ 18 = 19.722 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 5, 71 and 355.

Prime factorization of 355

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

The primes you divided by give 355 = 5 × 71. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 355

• 355 is a composite number.
• The sum of all its factors is 432; the sum of its proper factors (excluding 355) is 77, which makes it a deficient number (its proper factors add up to less than itself).
• 355 is not a perfect square, so its factors pair up evenly.
• Multiples of 355 include 710, 1,065, 1,420, 1,775 and so on.

Factors vs. multiples

Factors of 355 are the numbers that divide into it; multiples of 355 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.