Factor Calculator

Factors of 1002

The factors of 1002 are 1, 2, 3, 6, 167, 334, 501, and 1002. In total, 1002 has 8 factors. Its prime factorization is 2 × 3 × 167, and the sum of all its factors is 2016.

All factors of 1002

Here are all 8 factors of 1002, listed from smallest to largest.

12361673345011002

Factor pairs of 1002

These 4 pairs of whole numbers each multiply to give 1002.

1 × 1002 = 1002
2 × 501 = 1002
3 × 334 = 1002
6 × 167 = 1002

Prime factorization of 1002

Dividing 1002 by the smallest prime at each step gives its prime factorization:

1002 ÷ 2 = 501
501 ÷ 3 = 167
167 ÷ 167 = 1
Result: 1002 = 2 × 3 × 167 = 2 × 3 × 167

The distinct prime factors of 1002 are 2, 3, 167. To factorize any other number, use the prime factorization calculator.

Factor tree of 1002

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

Factor tree of 1002100225013167
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1002

Number of factors8
Sum of factors2016
Sum of proper factors1014
Prime factorization2 × 3 × 167
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 1002 interesting

  • 1002 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 1002 is an abundant number: its proper factors sum to 1014, which is 12 more than 1002 itself.
  • 1002 has 3 distinct prime factors (2, 3, 167), which is why it has so many divisors.

How to find the factors of 1002 yourself

Divide 1002 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 √1002 ≈ 31.65, because every factor above that pairs with one below it.

1002 ÷ 1 = 1002 ✓
1002 ÷ 2 = 501 ✓
1002 ÷ 3 = 334 ✓
1002 ÷ 6 = 167 ✓

Reading both columns gives every factor: 1, 2, 3, 6, 167, 334, 501, 1002. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1002.

Frequently asked questions about 1002

What are the factors of 1002?

The factors of 1002 are 1, 2, 3, 6, 167, 334, 501, and 1002. That is 8 factors in total, counting both 1 and 1002.

Is 1002 a prime number?

No, 1002 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 1002 is also divisible by 2.

What is the prime factorization of 1002?

The prime factorization of 1002 is 2 × 3 × 167. Written out in full: 2 × 3 × 167 = 1002. Its distinct prime factors are 2, 3, 167.

What two numbers multiply to give 1002?

There are 4 pairs of whole numbers that multiply to 1002: 1 × 1002, 2 × 501, 3 × 334, 6 × 167.

What is the sum of the factors of 1002?

Adding all the factors of 1002 together gives 2016. Excluding 1002 itself, the proper factors sum to 1014.

Is 1002 a perfect square?

No, 1002 is not a perfect square. There is no whole number that multiplies by itself to give 1002. The nearest perfect squares are 961 and 1024.

What is the largest factor of 1002 other than itself?

The largest factor of 1002 apart from 1002 itself is 501, since 1002 ÷ 501 = 2.

How many factors does 1002 have?

1002 has 8 factors: 1, 2, 3, 6, 167, 334, 501, and 1002. You can verify this from the prime factorization 2 × 3 × 167: add 1 to each exponent and multiply, giving 2 × 2 × 2 = 8.

Explore more

Try another number in the factor calculator, break 1002 down further with the prime factorization calculator, or compare 1002 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.