Factor Calculator

Factors of 1000

The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000. In total, 1000 has 16 factors. Its prime factorization is 2³ × 5³, and the sum of all its factors is 2340.

All factors of 1000

Here are all 16 factors of 1000, listed from smallest to largest.

1245810202540501001252002505001000

Factor pairs of 1000

These 8 pairs of whole numbers each multiply to give 1000.

1 × 1000 = 1000
2 × 500 = 1000
4 × 250 = 1000
5 × 200 = 1000
8 × 125 = 1000
10 × 100 = 1000
20 × 50 = 1000
25 × 40 = 1000

Prime factorization of 1000

Dividing 1000 by the smallest prime at each step gives its prime factorization:

1000 ÷ 2 = 500
500 ÷ 2 = 250
250 ÷ 2 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
Result: 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 2³ × 5³

The distinct prime factors of 1000 are 2, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 1000

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

Factor tree of 1000100025002250212552555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1000

Number of factors16
Sum of factors2340
Sum of proper factors1340
Prime factorization2³ × 5³
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?Yes (10³)
ClassificationAbundant

What makes 1000 interesting

  • 1000 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 8 different ways.
  • 1000 is a perfect cube: 10 × 10 × 10 = 1000.
  • 1000 is an abundant number: its proper factors sum to 1340, which is 340 more than 1000 itself.

How to find the factors of 1000 yourself

Divide 1000 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 √1000 ≈ 31.62, because every factor above that pairs with one below it.

1000 ÷ 1 = 1000 ✓
1000 ÷ 2 = 500 ✓
1000 ÷ 4 = 250 ✓
1000 ÷ 5 = 200 ✓
1000 ÷ 8 = 125 ✓
1000 ÷ 10 = 100 ✓
1000 ÷ 20 = 50 ✓
1000 ÷ 25 = 40 ✓

Reading both columns gives every factor: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1000.

Frequently asked questions about 1000

What are the factors of 1000?

The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000. That is 16 factors in total, counting both 1 and 1000.

Is 1000 a prime number?

No, 1000 is not prime — it is a composite number with 16 factors. A prime number has exactly two factors, but 1000 is also divisible by 2.

What is the prime factorization of 1000?

The prime factorization of 1000 is 2³ × 5³. Written out in full: 2 × 2 × 2 × 5 × 5 × 5 = 1000. Its distinct prime factors are 2, 5.

What two numbers multiply to give 1000?

There are 8 pairs of whole numbers that multiply to 1000: 1 × 1000, 2 × 500, 4 × 250, 5 × 200, 8 × 125, 10 × 100, 20 × 50, 25 × 40.

What is the sum of the factors of 1000?

Adding all the factors of 1000 together gives 2340. Excluding 1000 itself, the proper factors sum to 1340.

Is 1000 a perfect square?

No, 1000 is not a perfect square. There is no whole number that multiplies by itself to give 1000. The nearest perfect squares are 961 and 1024.

What is the largest factor of 1000 other than itself?

The largest factor of 1000 apart from 1000 itself is 500, since 1000 ÷ 500 = 2.

How many factors does 1000 have?

1000 has 16 factors: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000. You can verify this from the prime factorization 2³ × 5³: add 1 to each exponent and multiply, giving 4 × 4 = 16.

Explore more

Try another number in the factor calculator, break 1000 down further with the prime factorization calculator, or compare 1000 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.