Factor Calculator

Factors of 1007

The factors of 1007 are 1, 19, 53, and 1007. In total, 1007 has 4 factors. Its prime factorization is 19 × 53, and the sum of all its factors is 1080.

All factors of 1007

Here are all 4 factors of 1007, listed from smallest to largest.

119531007

Factor pairs of 1007

These 2 pairs of whole numbers each multiply to give 1007.

1 × 1007 = 1007
19 × 53 = 1007

Prime factorization of 1007

Dividing 1007 by the smallest prime at each step gives its prime factorization:

1007 ÷ 19 = 53
53 ÷ 53 = 1
Result: 1007 = 19 × 53 = 19 × 53

The distinct prime factors of 1007 are 19, 53. To factorize any other number, use the prime factorization calculator.

Factor tree of 1007

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

Factor tree of 100710071953
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1007

Number of factors4
Sum of factors1080
Sum of proper factors73
Prime factorization19 × 53
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 1007 interesting

  • 1007 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.
  • 1007 is a deficient number: its proper factors sum to 73, which is 934 less than 1007 itself.

How to find the factors of 1007 yourself

Divide 1007 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 √1007 ≈ 31.73, because every factor above that pairs with one below it.

1007 ÷ 1 = 1007 ✓
1007 ÷ 19 = 53 ✓

Reading both columns gives every factor: 1, 19, 53, 1007. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1007.

Frequently asked questions about 1007

What are the factors of 1007?

The factors of 1007 are 1, 19, 53, and 1007. That is 4 factors in total, counting both 1 and 1007.

Is 1007 a prime number?

No, 1007 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 1007 is also divisible by 19.

What is the prime factorization of 1007?

The prime factorization of 1007 is 19 × 53. Written out in full: 19 × 53 = 1007. Its distinct prime factors are 19, 53.

What two numbers multiply to give 1007?

There are 2 pairs of whole numbers that multiply to 1007: 1 × 1007, 19 × 53.

What is the sum of the factors of 1007?

Adding all the factors of 1007 together gives 1080. Excluding 1007 itself, the proper factors sum to 73.

Is 1007 a perfect square?

No, 1007 is not a perfect square. There is no whole number that multiplies by itself to give 1007. The nearest perfect squares are 961 and 1024.

What is the largest factor of 1007 other than itself?

The largest factor of 1007 apart from 1007 itself is 53, since 1007 ÷ 53 = 19.

How many factors does 1007 have?

1007 has 4 factors: 1, 19, 53, and 1007. You can verify this from the prime factorization 19 × 53: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 1007 down further with the prime factorization calculator, or compare 1007 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.