Factors of 420
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420. In total, 420 has 24 factors. Its prime factorization is 2² × 3 × 5 × 7, and the sum of all its factors is 1344.
All factors of 420
Here are all 24 factors of 420, listed from smallest to largest.
Factor pairs of 420
These 12 pairs of whole numbers each multiply to give 420.
Prime factorization of 420
Dividing 420 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 420 are 2, 3, 5, 7. To factorize any other number, use the prime factorization calculator.
Factor tree of 420
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 420
| Number of factors | 24 |
|---|---|
| Sum of factors | 1344 |
| Sum of proper factors | 924 |
| Prime factorization | 2² × 3 × 5 × 7 |
| Prime or composite? | Composite |
| Even or odd? | Even |
| Perfect square? | No |
| Perfect cube? | No |
| Classification | Abundant |
What makes 420 interesting
- 420 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 12 different ways.
- 420 is an abundant number: its proper factors sum to 924, which is 504 more than 420 itself.
- 420 has 4 distinct prime factors (2, 3, 5, 7), which is why it has so many divisors.
How to find the factors of 420 yourself
Divide 420 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 √420 ≈ 20.49, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 420.
Frequently asked questions about 420
What are the factors of 420?
Is 420 a prime number?
What is the prime factorization of 420?
What two numbers multiply to give 420?
What is the sum of the factors of 420?
Is 420 a perfect square?
What is the largest factor of 420 other than itself?
How many factors does 420 have?
Explore more
Try another number in the factor calculator, break 420 down further with the prime factorization calculator, or compare 420 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.