Factors of 84

How to find the factors of 84

Test every whole number from 1 up to the square root of 84 (√84 ≈ 9.165). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 84 ÷ 1 = 84 — so 1 and 84 are factors
• 84 ÷ 2 = 42 — so 2 and 42 are factors
• 84 ÷ 3 = 28 — so 3 and 28 are factors
• 84 ÷ 4 = 21 — so 4 and 21 are factors
• 84 ÷ 5 = 16.8 — not a whole number
• 84 ÷ 6 = 14 — so 6 and 14 are factors
• 84 ÷ 7 = 12 — so 7 and 12 are factors
• 84 ÷ 8 = 10.5 — not a whole number
• 84 ÷ 9 = 9.333 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.

Prime factorization of 84

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

The primes you divided by give 84 = 2² × 3 × 7. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) × (1 + 1) = 12.

Properties of 84

• 84 is a composite number.
• The sum of all its factors is 224; the sum of its proper factors (excluding 84) is 140, which makes it a abundant number (its proper factors add up to more than itself).
• 84 is not a perfect square, so its factors pair up evenly.
• Multiples of 84 include 168, 252, 336, 420 and so on.

Factors vs. multiples

Factors of 84 are the numbers that divide into it; multiples of 84 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.