Factors of 441

How to find the factors of 441

Test every whole number from 1 up to the square root of 441 (√441 ≈ 21.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 441 ÷ 1 = 441 — so 1 and 441 are factors
• 441 ÷ 2 = 220.5 — not a whole number
• 441 ÷ 3 = 147 — so 3 and 147 are factors
• 441 ÷ 4 = 110.25 — not a whole number
• 441 ÷ 5 = 88.2 — not a whole number
• 441 ÷ 6 = 73.5 — not a whole number
• 441 ÷ 7 = 63 — so 7 and 63 are factors
• 441 ÷ 8 = 55.125 — not a whole number
• 441 ÷ 9 = 49 — so 9 and 49 are factors
• 441 ÷ 10 = 44.1 — not a whole number
• 441 ÷ 11 = 40.091 — not a whole number
• 441 ÷ 12 = 36.75 — not a whole number
• 441 ÷ 13 = 33.923 — not a whole number
• 441 ÷ 14 = 31.5 — not a whole number
• 441 ÷ 15 = 29.4 — not a whole number
• 441 ÷ 16 = 27.563 — not a whole number
• 441 ÷ 17 = 25.941 — not a whole number
• 441 ÷ 18 = 24.5 — not a whole number
• 441 ÷ 19 = 23.211 — not a whole number
• 441 ÷ 20 = 22.05 — not a whole number
• 441 ÷ 21 = 21 — so 21 and 21 are factors

Collecting both numbers from every successful division gives the complete list: 1, 3, 7, 9, 21, 49, 63, 147 and 441.

Prime factorization of 441

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

The primes you divided by give 441 = 3² × 7². From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) = 9.

Properties of 441

• 441 is a composite number.
• The sum of all its factors is 741; the sum of its proper factors (excluding 441) is 300, which makes it a deficient number (its proper factors add up to less than itself).
• 441 is a perfect square: 21 × 21. Perfect squares always have an odd number of factors.
• Multiples of 441 include 882, 1,323, 1,764, 2,205 and so on.

Factors vs. multiples

Factors of 441 are the numbers that divide into it; multiples of 441 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.