Factors of 448

How to find the factors of 448

Test every whole number from 1 up to the square root of 448 (√448 ≈ 21.166). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 448 ÷ 1 = 448 — so 1 and 448 are factors
• 448 ÷ 2 = 224 — so 2 and 224 are factors
• 448 ÷ 3 = 149.333 — not a whole number
• 448 ÷ 4 = 112 — so 4 and 112 are factors
• 448 ÷ 5 = 89.6 — not a whole number
• 448 ÷ 6 = 74.667 — not a whole number
• 448 ÷ 7 = 64 — so 7 and 64 are factors
• 448 ÷ 8 = 56 — so 8 and 56 are factors
• 448 ÷ 9 = 49.778 — not a whole number
• 448 ÷ 10 = 44.8 — not a whole number
• 448 ÷ 11 = 40.727 — not a whole number
• 448 ÷ 12 = 37.333 — not a whole number
• 448 ÷ 13 = 34.462 — not a whole number
• 448 ÷ 14 = 32 — so 14 and 32 are factors
• 448 ÷ 15 = 29.867 — not a whole number
• 448 ÷ 16 = 28 — so 16 and 28 are factors
• 448 ÷ 17 = 26.353 — not a whole number
• 448 ÷ 18 = 24.889 — not a whole number
• 448 ÷ 19 = 23.579 — not a whole number
• 448 ÷ 20 = 22.4 — not a whole number
• 448 ÷ 21 = 21.333 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224 and 448.

Prime factorization of 448

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

The primes you divided by give 448 = 2⁶ × 7. From the exponents you can also count the factors without listing them: (6 + 1) × (1 + 1) = 14.

Properties of 448

• 448 is a composite number.
• The sum of all its factors is 1,016; the sum of its proper factors (excluding 448) is 568, which makes it a abundant number (its proper factors add up to more than itself).
• 448 is not a perfect square, so its factors pair up evenly.
• Multiples of 448 include 896, 1,344, 1,792, 2,240 and so on.

Factors vs. multiples

Factors of 448 are the numbers that divide into it; multiples of 448 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.