Factors of 315
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315. In total, 315 has 12 factors. Its prime factorization is 3² × 5 × 7, and the sum of all its factors is 624.
All factors of 315
Here are all 12 factors of 315, listed from smallest to largest.
Factor pairs of 315
These 6 pairs of whole numbers each multiply to give 315.
Prime factorization of 315
Dividing 315 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 315 are 3, 5, 7. To factorize any other number, use the prime factorization calculator.
Factor tree of 315
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 315
| Number of factors | 12 |
|---|---|
| Sum of factors | 624 |
| Sum of proper factors | 309 |
| Prime factorization | 3² × 5 × 7 |
| Prime or composite? | Composite |
| Even or odd? | Odd |
| Perfect square? | No |
| Perfect cube? | No |
| Classification | Deficient |
What makes 315 interesting
- 315 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.
- 315 is a deficient number: its proper factors sum to 309, which is 6 less than 315 itself.
- 315 has 3 distinct prime factors (3, 5, 7), which is why it has so many divisors.
How to find the factors of 315 yourself
Divide 315 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 √315 ≈ 17.75, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 315.
Frequently asked questions about 315
What are the factors of 315?
Is 315 a prime number?
What is the prime factorization of 315?
What two numbers multiply to give 315?
What is the sum of the factors of 315?
Is 315 a perfect square?
What is the largest factor of 315 other than itself?
How many factors does 315 have?
Explore more
Try another number in the factor calculator, break 315 down further with the prime factorization calculator, or compare 315 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.