Factors of 1008
The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, and 1008. In total, 1008 has 30 factors. Its prime factorization is 2⁴ × 3² × 7, and the sum of all its factors is 3224.
All factors of 1008
Here are all 30 factors of 1008, listed from smallest to largest.
Factor pairs of 1008
These 15 pairs of whole numbers each multiply to give 1008.
Prime factorization of 1008
Dividing 1008 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 1008 are 2, 3, 7. To factorize any other number, use the prime factorization calculator.
Factor tree of 1008
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 1008
| Number of factors | 30 |
|---|---|
| Sum of factors | 3224 |
| Sum of proper factors | 2216 |
| Prime factorization | 2⁴ × 3² × 7 |
| Prime or composite? | Composite |
| Even or odd? | Even |
| Perfect square? | No |
| Perfect cube? | No |
| Classification | Abundant |
What makes 1008 interesting
- 1008 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 15 different ways.
- 1008 is an abundant number: its proper factors sum to 2216, which is 1208 more than 1008 itself.
- 1008 has 3 distinct prime factors (2, 3, 7), which is why it has so many divisors.
How to find the factors of 1008 yourself
Divide 1008 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 √1008 ≈ 31.75, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 1008.
Frequently asked questions about 1008
What are the factors of 1008?
Is 1008 a prime number?
What is the prime factorization of 1008?
What two numbers multiply to give 1008?
What is the sum of the factors of 1008?
Is 1008 a perfect square?
What is the largest factor of 1008 other than itself?
How many factors does 1008 have?
Explore more
Try another number in the factor calculator, break 1008 down further with the prime factorization calculator, or compare 1008 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.