Factor Calculator

Factors of 765

The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, and 765. In total, 765 has 12 factors. Its prime factorization is 3² × 5 × 17, and the sum of all its factors is 1404.

All factors of 765

Here are all 12 factors of 765, listed from smallest to largest.

13591517455185153255765

Factor pairs of 765

These 6 pairs of whole numbers each multiply to give 765.

1 × 765 = 765
3 × 255 = 765
5 × 153 = 765
9 × 85 = 765
15 × 51 = 765
17 × 45 = 765

Prime factorization of 765

Dividing 765 by the smallest prime at each step gives its prime factorization:

765 ÷ 3 = 255
255 ÷ 3 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
Result: 765 = 3 × 3 × 5 × 17 = 3² × 5 × 17

The distinct prime factors of 765 are 3, 5, 17. To factorize any other number, use the prime factorization calculator.

Factor tree of 765

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

Factor tree of 7657653255385517
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 765

Number of factors12
Sum of factors1404
Sum of proper factors639
Prime factorization3² × 5 × 17
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 765 interesting

  • 765 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 765 is a deficient number: its proper factors sum to 639, which is 126 less than 765 itself.
  • 765 has 3 distinct prime factors (3, 5, 17), which is why it has so many divisors.

How to find the factors of 765 yourself

Divide 765 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 √765 ≈ 27.66, because every factor above that pairs with one below it.

765 ÷ 1 = 765 ✓
765 ÷ 3 = 255 ✓
765 ÷ 5 = 153 ✓
765 ÷ 9 = 85 ✓
765 ÷ 15 = 51 ✓
765 ÷ 17 = 45 ✓

Reading both columns gives every factor: 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765. The factor calculator does this automatically for any number.

Numbers mathematically connected to 765.

Frequently asked questions about 765

What are the factors of 765?

The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, and 765. That is 12 factors in total, counting both 1 and 765.

Is 765 a prime number?

No, 765 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 765 is also divisible by 3.

What is the prime factorization of 765?

The prime factorization of 765 is 3² × 5 × 17. Written out in full: 3 × 3 × 5 × 17 = 765. Its distinct prime factors are 3, 5, 17.

What two numbers multiply to give 765?

There are 6 pairs of whole numbers that multiply to 765: 1 × 765, 3 × 255, 5 × 153, 9 × 85, 15 × 51, 17 × 45.

What is the sum of the factors of 765?

Adding all the factors of 765 together gives 1404. Excluding 765 itself, the proper factors sum to 639.

Is 765 a perfect square?

No, 765 is not a perfect square. There is no whole number that multiplies by itself to give 765. The nearest perfect squares are 729 and 784.

What is the largest factor of 765 other than itself?

The largest factor of 765 apart from 765 itself is 255, since 765 ÷ 255 = 3.

How many factors does 765 have?

765 has 12 factors: 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, and 765. You can verify this from the prime factorization 3² × 5 × 17: add 1 to each exponent and multiply, giving 3 × 2 × 2 = 12.

Explore more

Try another number in the factor calculator, break 765 down further with the prime factorization calculator, or compare 765 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.