Factors of 361

How to find the factors of 361

Test every whole number from 1 up to the square root of 361 (√361 ≈ 19.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 361 ÷ 1 = 361 — so 1 and 361 are factors
• 361 ÷ 2 = 180.5 — not a whole number
• 361 ÷ 3 = 120.333 — not a whole number
• 361 ÷ 4 = 90.25 — not a whole number
• 361 ÷ 5 = 72.2 — not a whole number
• 361 ÷ 6 = 60.167 — not a whole number
• 361 ÷ 7 = 51.571 — not a whole number
• 361 ÷ 8 = 45.125 — not a whole number
• 361 ÷ 9 = 40.111 — not a whole number
• 361 ÷ 10 = 36.1 — not a whole number
• 361 ÷ 11 = 32.818 — not a whole number
• 361 ÷ 12 = 30.083 — not a whole number
• 361 ÷ 13 = 27.769 — not a whole number
• 361 ÷ 14 = 25.786 — not a whole number
• 361 ÷ 15 = 24.067 — not a whole number
• 361 ÷ 16 = 22.563 — not a whole number
• 361 ÷ 17 = 21.235 — not a whole number
• 361 ÷ 18 = 20.056 — not a whole number
• 361 ÷ 19 = 19 — so 19 and 19 are factors

Collecting both numbers from every successful division gives the complete list: 1, 19 and 361.

Prime factorization of 361

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

The primes you divided by give 361 = 19². From the exponents you can also count the factors without listing them: (2 + 1) = 3.

Properties of 361

• 361 is a composite number.
• The sum of all its factors is 381; the sum of its proper factors (excluding 361) is 20, which makes it a deficient number (its proper factors add up to less than itself).
• 361 is a perfect square: 19 × 19. Perfect squares always have an odd number of factors.
• Multiples of 361 include 722, 1,083, 1,444, 1,805 and so on.

Factors vs. multiples

Factors of 361 are the numbers that divide into it; multiples of 361 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.