Factor Calculator

Factors of 945

The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945. In total, 945 has 16 factors. Its prime factorization is 3³ × 5 × 7, and the sum of all its factors is 1920.

All factors of 945

Here are all 16 factors of 945, listed from smallest to largest.

13579152127354563105135189315945

Factor pairs of 945

These 8 pairs of whole numbers each multiply to give 945.

1 × 945 = 945
3 × 315 = 945
5 × 189 = 945
7 × 135 = 945
9 × 105 = 945
15 × 63 = 945
21 × 45 = 945
27 × 35 = 945

Prime factorization of 945

Dividing 945 by the smallest prime at each step gives its prime factorization:

945 ÷ 3 = 315
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
Result: 945 = 3 × 3 × 3 × 5 × 7 = 3³ × 5 × 7

The distinct prime factors of 945 are 3, 5, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 945

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

Factor tree of 9459453315310533557
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 945

Number of factors16
Sum of factors1920
Sum of proper factors975
Prime factorization3³ × 5 × 7
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 945 interesting

  • 945 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.
  • 945 is an abundant number: its proper factors sum to 975, which is 30 more than 945 itself.
  • 945 has 3 distinct prime factors (3, 5, 7), which is why it has so many divisors.

How to find the factors of 945 yourself

Divide 945 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 √945 ≈ 30.74, because every factor above that pairs with one below it.

945 ÷ 1 = 945 ✓
945 ÷ 3 = 315 ✓
945 ÷ 5 = 189 ✓
945 ÷ 7 = 135 ✓
945 ÷ 9 = 105 ✓
945 ÷ 15 = 63 ✓
945 ÷ 21 = 45 ✓
945 ÷ 27 = 35 ✓

Reading both columns gives every factor: 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945. The factor calculator does this automatically for any number.

Numbers mathematically connected to 945.

Frequently asked questions about 945

What are the factors of 945?

The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945. That is 16 factors in total, counting both 1 and 945.

Is 945 a prime number?

No, 945 is not prime — it is a composite number with 16 factors. A prime number has exactly two factors, but 945 is also divisible by 3.

What is the prime factorization of 945?

The prime factorization of 945 is 3³ × 5 × 7. Written out in full: 3 × 3 × 3 × 5 × 7 = 945. Its distinct prime factors are 3, 5, 7.

What two numbers multiply to give 945?

There are 8 pairs of whole numbers that multiply to 945: 1 × 945, 3 × 315, 5 × 189, 7 × 135, 9 × 105, 15 × 63, 21 × 45, 27 × 35.

What is the sum of the factors of 945?

Adding all the factors of 945 together gives 1920. Excluding 945 itself, the proper factors sum to 975.

Is 945 a perfect square?

No, 945 is not a perfect square. There is no whole number that multiplies by itself to give 945. The nearest perfect squares are 900 and 961.

What is the largest factor of 945 other than itself?

The largest factor of 945 apart from 945 itself is 315, since 945 ÷ 315 = 3.

How many factors does 945 have?

945 has 16 factors: 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945. You can verify this from the prime factorization 3³ × 5 × 7: add 1 to each exponent and multiply, giving 4 × 2 × 2 = 16.

Explore more

Try another number in the factor calculator, break 945 down further with the prime factorization calculator, or compare 945 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.