Factor Calculator

Factors of 1003

The factors of 1003 are 1, 17, 59, and 1003. In total, 1003 has 4 factors. Its prime factorization is 17 × 59, and the sum of all its factors is 1080.

All factors of 1003

Here are all 4 factors of 1003, listed from smallest to largest.

117591003

Factor pairs of 1003

These 2 pairs of whole numbers each multiply to give 1003.

1 × 1003 = 1003
17 × 59 = 1003

Prime factorization of 1003

Dividing 1003 by the smallest prime at each step gives its prime factorization:

1003 ÷ 17 = 59
59 ÷ 59 = 1
Result: 1003 = 17 × 59 = 17 × 59

The distinct prime factors of 1003 are 17, 59. To factorize any other number, use the prime factorization calculator.

Factor tree of 1003

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

Factor tree of 100310031759
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1003

Number of factors4
Sum of factors1080
Sum of proper factors77
Prime factorization17 × 59
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 1003 interesting

  • 1003 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
  • 1003 is a deficient number: its proper factors sum to 77, which is 926 less than 1003 itself.

How to find the factors of 1003 yourself

Divide 1003 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 √1003 ≈ 31.67, because every factor above that pairs with one below it.

1003 ÷ 1 = 1003 ✓
1003 ÷ 17 = 59 ✓

Reading both columns gives every factor: 1, 17, 59, 1003. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1003.

Frequently asked questions about 1003

What are the factors of 1003?

The factors of 1003 are 1, 17, 59, and 1003. That is 4 factors in total, counting both 1 and 1003.

Is 1003 a prime number?

No, 1003 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 1003 is also divisible by 17.

What is the prime factorization of 1003?

The prime factorization of 1003 is 17 × 59. Written out in full: 17 × 59 = 1003. Its distinct prime factors are 17, 59.

What two numbers multiply to give 1003?

There are 2 pairs of whole numbers that multiply to 1003: 1 × 1003, 17 × 59.

What is the sum of the factors of 1003?

Adding all the factors of 1003 together gives 1080. Excluding 1003 itself, the proper factors sum to 77.

Is 1003 a perfect square?

No, 1003 is not a perfect square. There is no whole number that multiplies by itself to give 1003. The nearest perfect squares are 961 and 1024.

What is the largest factor of 1003 other than itself?

The largest factor of 1003 apart from 1003 itself is 59, since 1003 ÷ 59 = 17.

How many factors does 1003 have?

1003 has 4 factors: 1, 17, 59, and 1003. You can verify this from the prime factorization 17 × 59: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 1003 down further with the prime factorization calculator, or compare 1003 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.