Factor Calculator

Factors of 840

The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840. In total, 840 has 32 factors. Its prime factorization is 2³ × 3 × 5 × 7, and the sum of all its factors is 2880.

All factors of 840

Here are all 32 factors of 840, listed from smallest to largest.

1234567810121415202124283035404256607084105120140168210280420840

Factor pairs of 840

These 16 pairs of whole numbers each multiply to give 840.

1 × 840 = 840
2 × 420 = 840
3 × 280 = 840
4 × 210 = 840
5 × 168 = 840
6 × 140 = 840
7 × 120 = 840
8 × 105 = 840
10 × 84 = 840
12 × 70 = 840
14 × 60 = 840
15 × 56 = 840
20 × 42 = 840
21 × 40 = 840
24 × 35 = 840
28 × 30 = 840

Prime factorization of 840

Dividing 840 by the smallest prime at each step gives its prime factorization:

840 ÷ 2 = 420
420 ÷ 2 = 210
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
Result: 840 = 2 × 2 × 2 × 3 × 5 × 7 = 2³ × 3 × 5 × 7

The distinct prime factors of 840 are 2, 3, 5, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 840

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 84084024202210210533557
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 840

Number of factors32
Sum of factors2880
Sum of proper factors2040
Prime factorization2³ × 3 × 5 × 7
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 840 interesting

  • 840 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 16 different ways.
  • 840 is an abundant number: its proper factors sum to 2040, which is 1200 more than 840 itself.
  • 840 is a highly composite number — it has more factors (32) than any smaller positive integer. Numbers like this are useful in measurement systems because they divide evenly so many ways.
  • 840 has 4 distinct prime factors (2, 3, 5, 7), which is why it has so many divisors.

How to find the factors of 840 yourself

Divide 840 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 √840 ≈ 28.98, because every factor above that pairs with one below it.

840 ÷ 1 = 840 ✓
840 ÷ 2 = 420 ✓
840 ÷ 3 = 280 ✓
840 ÷ 4 = 210 ✓
840 ÷ 5 = 168 ✓
840 ÷ 6 = 140 ✓
840 ÷ 7 = 120 ✓
840 ÷ 8 = 105 ✓
840 ÷ 10 = 84 ✓
840 ÷ 12 = 70 ✓
840 ÷ 14 = 60 ✓
840 ÷ 15 = 56 ✓
840 ÷ 20 = 42 ✓
840 ÷ 21 = 40 ✓
840 ÷ 24 = 35 ✓
840 ÷ 28 = 30 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840. The factor calculator does this automatically for any number.

Numbers mathematically connected to 840.

Frequently asked questions about 840

What are the factors of 840?

The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840. That is 32 factors in total, counting both 1 and 840.

Is 840 a prime number?

No, 840 is not prime — it is a composite number with 32 factors. A prime number has exactly two factors, but 840 is also divisible by 2.

What is the prime factorization of 840?

The prime factorization of 840 is 2³ × 3 × 5 × 7. Written out in full: 2 × 2 × 2 × 3 × 5 × 7 = 840. Its distinct prime factors are 2, 3, 5, 7.

What two numbers multiply to give 840?

There are 16 pairs of whole numbers that multiply to 840: 1 × 840, 2 × 420, 3 × 280, 4 × 210, 5 × 168, 6 × 140, 7 × 120, 8 × 105, 10 × 84, 12 × 70, 14 × 60, 15 × 56, 20 × 42, 21 × 40, 24 × 35, 28 × 30.

What is the sum of the factors of 840?

Adding all the factors of 840 together gives 2880. Excluding 840 itself, the proper factors sum to 2040.

Is 840 a perfect square?

No, 840 is not a perfect square. There is no whole number that multiplies by itself to give 840. The nearest perfect squares are 784 and 841.

What is the largest factor of 840 other than itself?

The largest factor of 840 apart from 840 itself is 420, since 840 ÷ 420 = 2.

How many factors does 840 have?

840 has 32 factors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840. You can verify this from the prime factorization 2³ × 3 × 5 × 7: add 1 to each exponent and multiply, giving 4 × 2 × 2 × 2 = 32.

Explore more

Try another number in the factor calculator, break 840 down further with the prime factorization calculator, or compare 840 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.