Factors of 363

How to find the factors of 363

Test every whole number from 1 up to the square root of 363 (√363 ≈ 19.053). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 363 ÷ 1 = 363 — so 1 and 363 are factors
• 363 ÷ 2 = 181.5 — not a whole number
• 363 ÷ 3 = 121 — so 3 and 121 are factors
• 363 ÷ 4 = 90.75 — not a whole number
• 363 ÷ 5 = 72.6 — not a whole number
• 363 ÷ 6 = 60.5 — not a whole number
• 363 ÷ 7 = 51.857 — not a whole number
• 363 ÷ 8 = 45.375 — not a whole number
• 363 ÷ 9 = 40.333 — not a whole number
• 363 ÷ 10 = 36.3 — not a whole number
• 363 ÷ 11 = 33 — so 11 and 33 are factors
• 363 ÷ 12 = 30.25 — not a whole number
• 363 ÷ 13 = 27.923 — not a whole number
• 363 ÷ 14 = 25.929 — not a whole number
• 363 ÷ 15 = 24.2 — not a whole number
• 363 ÷ 16 = 22.688 — not a whole number
• 363 ÷ 17 = 21.353 — not a whole number
• 363 ÷ 18 = 20.167 — not a whole number
• 363 ÷ 19 = 19.105 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 11, 33, 121 and 363.

Prime factorization of 363

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

The primes you divided by give 363 = 3 × 11². From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) = 6.

Properties of 363

• 363 is a composite number.
• The sum of all its factors is 532; the sum of its proper factors (excluding 363) is 169, which makes it a deficient number (its proper factors add up to less than itself).
• 363 is not a perfect square, so its factors pair up evenly.
• Multiples of 363 include 726, 1,089, 1,452, 1,815 and so on.

Factors vs. multiples

Factors of 363 are the numbers that divide into it; multiples of 363 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.