Factors of 350

How to find the factors of 350

Test every whole number from 1 up to the square root of 350 (√350 ≈ 18.708). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 350 ÷ 1 = 350 — so 1 and 350 are factors
• 350 ÷ 2 = 175 — so 2 and 175 are factors
• 350 ÷ 3 = 116.667 — not a whole number
• 350 ÷ 4 = 87.5 — not a whole number
• 350 ÷ 5 = 70 — so 5 and 70 are factors
• 350 ÷ 6 = 58.333 — not a whole number
• 350 ÷ 7 = 50 — so 7 and 50 are factors
• 350 ÷ 8 = 43.75 — not a whole number
• 350 ÷ 9 = 38.889 — not a whole number
• 350 ÷ 10 = 35 — so 10 and 35 are factors
• 350 ÷ 11 = 31.818 — not a whole number
• 350 ÷ 12 = 29.167 — not a whole number
• 350 ÷ 13 = 26.923 — not a whole number
• 350 ÷ 14 = 25 — so 14 and 25 are factors
• 350 ÷ 15 = 23.333 — not a whole number
• 350 ÷ 16 = 21.875 — not a whole number
• 350 ÷ 17 = 20.588 — not a whole number
• 350 ÷ 18 = 19.444 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350.

Prime factorization of 350

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

The primes you divided by give 350 = 2 × 5² × 7. From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) × (1 + 1) = 12.

Properties of 350

• 350 is a composite number.
• The sum of all its factors is 744; the sum of its proper factors (excluding 350) is 394, which makes it a abundant number (its proper factors add up to more than itself).
• 350 is not a perfect square, so its factors pair up evenly.
• Multiples of 350 include 700, 1,050, 1,400, 1,750 and so on.

Factors vs. multiples

Factors of 350 are the numbers that divide into it; multiples of 350 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.