Factors of 828

How to find the factors of 828

Test every whole number from 1 up to the square root of 828 (√828 ≈ 28.775). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 828 ÷ 1 = 828 — so 1 and 828 are factors
• 828 ÷ 2 = 414 — so 2 and 414 are factors
• 828 ÷ 3 = 276 — so 3 and 276 are factors
• 828 ÷ 4 = 207 — so 4 and 207 are factors
• 828 ÷ 5 = 165.6 — not a whole number
• 828 ÷ 6 = 138 — so 6 and 138 are factors
• 828 ÷ 7 = 118.286 — not a whole number
• 828 ÷ 8 = 103.5 — not a whole number
• 828 ÷ 9 = 92 — so 9 and 92 are factors
• 828 ÷ 10 = 82.8 — not a whole number
• 828 ÷ 11 = 75.273 — not a whole number
• 828 ÷ 12 = 69 — so 12 and 69 are factors
• 828 ÷ 13 = 63.692 — not a whole number
• 828 ÷ 14 = 59.143 — not a whole number
• 828 ÷ 15 = 55.2 — not a whole number
• 828 ÷ 16 = 51.75 — not a whole number
• 828 ÷ 17 = 48.706 — not a whole number
• 828 ÷ 18 = 46 — so 18 and 46 are factors
• 828 ÷ 19 = 43.579 — not a whole number
• 828 ÷ 20 = 41.4 — not a whole number
• 828 ÷ 21 = 39.429 — not a whole number
• 828 ÷ 22 = 37.636 — not a whole number
• 828 ÷ 23 = 36 — so 23 and 36 are factors
• 828 ÷ 24 = 34.5 — not a whole number
• 828 ÷ 25 = 33.12 — not a whole number
• 828 ÷ 26 = 31.846 — not a whole number
• 828 ÷ 27 = 30.667 — not a whole number
• 828 ÷ 28 = 29.571 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414 and 828.

Prime factorization of 828

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

The primes you divided by give 828 = 2² × 3² × 23. From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) × (1 + 1) = 18.

Properties of 828

• 828 is a composite number.
• The sum of all its factors is 2,184; the sum of its proper factors (excluding 828) is 1,356, which makes it a abundant number (its proper factors add up to more than itself).
• 828 is not a perfect square, so its factors pair up evenly.
• Multiples of 828 include 1,656, 2,484, 3,312, 4,140 and so on.

Factors vs. multiples

Factors of 828 are the numbers that divide into it; multiples of 828 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.