Factor Calculator

Factors of 1004

The factors of 1004 are 1, 2, 4, 251, 502, and 1004. In total, 1004 has 6 factors. Its prime factorization is 2² × 251, and the sum of all its factors is 1764.

All factors of 1004

Here are all 6 factors of 1004, listed from smallest to largest.

1242515021004

Factor pairs of 1004

These 3 pairs of whole numbers each multiply to give 1004.

1 × 1004 = 1004
2 × 502 = 1004
4 × 251 = 1004

Prime factorization of 1004

Dividing 1004 by the smallest prime at each step gives its prime factorization:

1004 ÷ 2 = 502
502 ÷ 2 = 251
251 ÷ 251 = 1
Result: 1004 = 2 × 2 × 251 = 2² × 251

The distinct prime factors of 1004 are 2, 251. To factorize any other number, use the prime factorization calculator.

Factor tree of 1004

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

Factor tree of 1004100425022251
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1004

Number of factors6
Sum of factors1764
Sum of proper factors760
Prime factorization2² × 251
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 1004 interesting

  • 1004 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 3 different ways.
  • 1004 is a deficient number: its proper factors sum to 760, which is 244 less than 1004 itself.

How to find the factors of 1004 yourself

Divide 1004 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 √1004 ≈ 31.69, because every factor above that pairs with one below it.

1004 ÷ 1 = 1004 ✓
1004 ÷ 2 = 502 ✓
1004 ÷ 4 = 251 ✓

Reading both columns gives every factor: 1, 2, 4, 251, 502, 1004. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1004.

Frequently asked questions about 1004

What are the factors of 1004?

The factors of 1004 are 1, 2, 4, 251, 502, and 1004. That is 6 factors in total, counting both 1 and 1004.

Is 1004 a prime number?

No, 1004 is not prime — it is a composite number with 6 factors. A prime number has exactly two factors, but 1004 is also divisible by 2.

What is the prime factorization of 1004?

The prime factorization of 1004 is 2² × 251. Written out in full: 2 × 2 × 251 = 1004. Its distinct prime factors are 2, 251.

What two numbers multiply to give 1004?

There are 3 pairs of whole numbers that multiply to 1004: 1 × 1004, 2 × 502, 4 × 251.

What is the sum of the factors of 1004?

Adding all the factors of 1004 together gives 1764. Excluding 1004 itself, the proper factors sum to 760.

Is 1004 a perfect square?

No, 1004 is not a perfect square. There is no whole number that multiplies by itself to give 1004. The nearest perfect squares are 961 and 1024.

What is the largest factor of 1004 other than itself?

The largest factor of 1004 apart from 1004 itself is 502, since 1004 ÷ 502 = 2.

How many factors does 1004 have?

1004 has 6 factors: 1, 2, 4, 251, 502, and 1004. You can verify this from the prime factorization 2² × 251: add 1 to each exponent and multiply, giving 3 × 2 = 6.

Explore more

Try another number in the factor calculator, break 1004 down further with the prime factorization calculator, or compare 1004 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.