Factor Calculator

Factors of 1053

The factors of 1053 are 1, 3, 9, 13, 27, 39, 81, 117, 351, and 1053. In total, 1053 has 10 factors. Its prime factorization is 3⁴ × 13, and the sum of all its factors is 1694.

All factors of 1053

Here are all 10 factors of 1053, listed from smallest to largest.

139132739811173511053

Factor pairs of 1053

These 5 pairs of whole numbers each multiply to give 1053.

1 × 1053 = 1053
3 × 351 = 1053
9 × 117 = 1053
13 × 81 = 1053
27 × 39 = 1053

Prime factorization of 1053

Dividing 1053 by the smallest prime at each step gives its prime factorization:

1053 ÷ 3 = 351
351 ÷ 3 = 117
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
Result: 1053 = 3 × 3 × 3 × 3 × 13 = 3⁴ × 13

The distinct prime factors of 1053 are 3, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 1053

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

Factor tree of 1053105333513117339313
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1053

Number of factors10
Sum of factors1694
Sum of proper factors641
Prime factorization3⁴ × 13
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 1053 interesting

  • 1053 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
  • 1053 is a deficient number: its proper factors sum to 641, which is 412 less than 1053 itself.

How to find the factors of 1053 yourself

Divide 1053 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 √1053 ≈ 32.45, because every factor above that pairs with one below it.

1053 ÷ 1 = 1053 ✓
1053 ÷ 3 = 351 ✓
1053 ÷ 9 = 117 ✓
1053 ÷ 13 = 81 ✓
1053 ÷ 27 = 39 ✓

Reading both columns gives every factor: 1, 3, 9, 13, 27, 39, 81, 117, 351, 1053. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1053.

Frequently asked questions about 1053

What are the factors of 1053?

The factors of 1053 are 1, 3, 9, 13, 27, 39, 81, 117, 351, and 1053. That is 10 factors in total, counting both 1 and 1053.

Is 1053 a prime number?

No, 1053 is not prime — it is a composite number with 10 factors. A prime number has exactly two factors, but 1053 is also divisible by 3.

What is the prime factorization of 1053?

The prime factorization of 1053 is 3⁴ × 13. Written out in full: 3 × 3 × 3 × 3 × 13 = 1053. Its distinct prime factors are 3, 13.

What two numbers multiply to give 1053?

There are 5 pairs of whole numbers that multiply to 1053: 1 × 1053, 3 × 351, 9 × 117, 13 × 81, 27 × 39.

What is the sum of the factors of 1053?

Adding all the factors of 1053 together gives 1694. Excluding 1053 itself, the proper factors sum to 641.

Is 1053 a perfect square?

No, 1053 is not a perfect square. There is no whole number that multiplies by itself to give 1053. The nearest perfect squares are 1024 and 1089.

What is the largest factor of 1053 other than itself?

The largest factor of 1053 apart from 1053 itself is 351, since 1053 ÷ 351 = 3.

How many factors does 1053 have?

1053 has 10 factors: 1, 3, 9, 13, 27, 39, 81, 117, 351, and 1053. You can verify this from the prime factorization 3⁴ × 13: add 1 to each exponent and multiply, giving 5 × 2 = 10.

Explore more

Try another number in the factor calculator, break 1053 down further with the prime factorization calculator, or compare 1053 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.