Factors of 126
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126. In total, 126 has 12 factors. Its prime factorization is 2 × 3² × 7, and the sum of all its factors is 312.
All factors of 126
Here are all 12 factors of 126, listed from smallest to largest.
Factor pairs of 126
These 6 pairs of whole numbers each multiply to give 126.
Prime factorization of 126
Dividing 126 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 126 are 2, 3, 7. To factorize any other number, use the prime factorization calculator.
Factor tree of 126
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 126
| Number of factors | 12 |
|---|---|
| Sum of factors | 312 |
| Sum of proper factors | 186 |
| Prime factorization | 2 × 3² × 7 |
| Prime or composite? | Composite |
| Even or odd? | Even |
| Perfect square? | No |
| Perfect cube? | No |
| Classification | Abundant |
What makes 126 interesting
- 126 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.
- 126 is an abundant number: its proper factors sum to 186, which is 60 more than 126 itself.
- 126 has 3 distinct prime factors (2, 3, 7), which is why it has so many divisors.
How to find the factors of 126 yourself
Divide 126 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 √126 ≈ 11.22, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 126.
Frequently asked questions about 126
What are the factors of 126?
Is 126 a prime number?
What is the prime factorization of 126?
What two numbers multiply to give 126?
What is the sum of the factors of 126?
Is 126 a perfect square?
What is the largest factor of 126 other than itself?
How many factors does 126 have?
Explore more
Try another number in the factor calculator, break 126 down further with the prime factorization calculator, or compare 126 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.