Factors of 301

How to find the factors of 301

Test every whole number from 1 up to the square root of 301 (√301 ≈ 17.349). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 301 ÷ 1 = 301 — so 1 and 301 are factors
• 301 ÷ 2 = 150.5 — not a whole number
• 301 ÷ 3 = 100.333 — not a whole number
• 301 ÷ 4 = 75.25 — not a whole number
• 301 ÷ 5 = 60.2 — not a whole number
• 301 ÷ 6 = 50.167 — not a whole number
• 301 ÷ 7 = 43 — so 7 and 43 are factors
• 301 ÷ 8 = 37.625 — not a whole number
• 301 ÷ 9 = 33.444 — not a whole number
• 301 ÷ 10 = 30.1 — not a whole number
• 301 ÷ 11 = 27.364 — not a whole number
• 301 ÷ 12 = 25.083 — not a whole number
• 301 ÷ 13 = 23.154 — not a whole number
• 301 ÷ 14 = 21.5 — not a whole number
• 301 ÷ 15 = 20.067 — not a whole number
• 301 ÷ 16 = 18.813 — not a whole number
• 301 ÷ 17 = 17.706 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 7, 43 and 301.

Prime factorization of 301

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

The primes you divided by give 301 = 7 × 43. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 301

• 301 is a composite number.
• The sum of all its factors is 352; the sum of its proper factors (excluding 301) is 51, which makes it a deficient number (its proper factors add up to less than itself).
• 301 is not a perfect square, so its factors pair up evenly.
• Multiples of 301 include 602, 903, 1,204, 1,505 and so on.

Factors vs. multiples

Factors of 301 are the numbers that divide into it; multiples of 301 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.