Factor Calculator

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.

123467121421284284

Factor pairs of 84

These 6 pairs of whole numbers each multiply to give 84.

1 × 84 = 84
2 × 42 = 84
3 × 28 = 84
4 × 21 = 84
6 × 14 = 84
7 × 12 = 84

Prime factorization of 84

Dividing 84 by the smallest prime at each step gives its prime factorization:

84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
Result: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7

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.

Factor tree of 848424222137
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 84

Number of factors12
Sum of factors224
Sum of proper factors140
Prime factorization2² × 3 × 7
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

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 √849.17, because every factor above that pairs with one below it.

84 ÷ 1 = 84
84 ÷ 2 = 42
84 ÷ 3 = 28
84 ÷ 4 = 21
84 ÷ 6 = 14
84 ÷ 7 = 12

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.

Frequently asked questions about 84

What are the factors of 84?

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. That is 12 factors in total, counting both 1 and 84.

Is 84 a prime number?

No, 84 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 84 is also divisible by 2.

What is the prime factorization of 84?

The prime factorization of 84 is 2² × 3 × 7. Written out in full: 2 × 2 × 3 × 7 = 84. Its distinct prime factors are 2, 3, 7.

What two numbers multiply to give 84?

There are 6 pairs of whole numbers that multiply to 84: 1 × 84, 2 × 42, 3 × 28, 4 × 21, 6 × 14, 7 × 12.

What is the sum of the factors of 84?

Adding all the factors of 84 together gives 224. Excluding 84 itself, the proper factors sum to 140.

Is 84 a perfect square?

No, 84 is not a perfect square. There is no whole number that multiplies by itself to give 84. The nearest perfect squares are 81 and 100.

What is the largest factor of 84 other than itself?

The largest factor of 84 apart from 84 itself is 42, since 84 ÷ 42 = 2.

How many factors does 84 have?

84 has 12 factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. You can verify this from the prime factorization 2² × 3 × 7: add 1 to each exponent and multiply, giving 3 × 2 × 2 = 12.

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.