Factors of 84
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. In total, 84 has 12 factors. Its prime factorization is 2² × 3 × 7, and the sum of all its factors is 224.
All factors of 84
Here are all 12 factors of 84, listed from smallest to largest.
Factor pairs of 84
These 6 pairs of whole numbers each multiply to give 84.
Prime factorization of 84
Dividing 84 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 84 are 2, 3, 7. To factorize any other number, use the prime factorization calculator.
Factor tree of 84
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 84
| Number of factors | 12 |
|---|---|
| Sum of factors | 224 |
| Sum of proper factors | 140 |
| Prime factorization | 2² × 3 × 7 |
| Prime or composite? | Composite |
| Even or odd? | Even |
| Perfect square? | No |
| Perfect cube? | No |
| Classification | Abundant |
What makes 84 interesting
- 84 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
- 84 is an abundant number: its proper factors sum to 140, which is 56 more than 84 itself.
- 84 has 3 distinct prime factors (2, 3, 7), which is why it has so many divisors.
How to find the factors of 84 yourself
Divide 84 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √84 ≈ 9.17, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 84.
Frequently asked questions about 84
What are the factors of 84?
Is 84 a prime number?
What is the prime factorization of 84?
What two numbers multiply to give 84?
What is the sum of the factors of 84?
Is 84 a perfect square?
What is the largest factor of 84 other than itself?
How many factors does 84 have?
Explore more
Try another number in the factor calculator, break 84 down further with the prime factorization calculator, or compare 84 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.