Factors of 300

How to find the factors of 300

Test every whole number from 1 up to the square root of 300 (√300 ≈ 17.321). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 300 ÷ 1 = 300 — so 1 and 300 are factors
• 300 ÷ 2 = 150 — so 2 and 150 are factors
• 300 ÷ 3 = 100 — so 3 and 100 are factors
• 300 ÷ 4 = 75 — so 4 and 75 are factors
• 300 ÷ 5 = 60 — so 5 and 60 are factors
• 300 ÷ 6 = 50 — so 6 and 50 are factors
• 300 ÷ 7 = 42.857 — not a whole number
• 300 ÷ 8 = 37.5 — not a whole number
• 300 ÷ 9 = 33.333 — not a whole number
• 300 ÷ 10 = 30 — so 10 and 30 are factors
• 300 ÷ 11 = 27.273 — not a whole number
• 300 ÷ 12 = 25 — so 12 and 25 are factors
• 300 ÷ 13 = 23.077 — not a whole number
• 300 ÷ 14 = 21.429 — not a whole number
• 300 ÷ 15 = 20 — so 15 and 20 are factors
• 300 ÷ 16 = 18.75 — not a whole number
• 300 ÷ 17 = 17.647 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 and 300.

Prime factorization of 300

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

The primes you divided by give 300 = 2² × 3 × 5². From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) × (2 + 1) = 18.

Properties of 300

• 300 is a composite number.
• The sum of all its factors is 868; the sum of its proper factors (excluding 300) is 568, which makes it a abundant number (its proper factors add up to more than itself).
• 300 is not a perfect square, so its factors pair up evenly.
• Multiples of 300 include 600, 900, 1,200, 1,500 and so on.

Factors vs. multiples

Factors of 300 are the numbers that divide into it; multiples of 300 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.