Factor Calculator

Factors of 786

The factors of 786 are 1, 2, 3, 6, 131, 262, 393, and 786. In total, 786 has 8 factors. Its prime factorization is 2 × 3 × 131, and the sum of all its factors is 1584.

All factors of 786

Here are all 8 factors of 786, listed from smallest to largest.

1236131262393786

Factor pairs of 786

These 4 pairs of whole numbers each multiply to give 786.

1 × 786 = 786
2 × 393 = 786
3 × 262 = 786
6 × 131 = 786

Prime factorization of 786

Dividing 786 by the smallest prime at each step gives its prime factorization:

786 ÷ 2 = 393
393 ÷ 3 = 131
131 ÷ 131 = 1
Result: 786 = 2 × 3 × 131 = 2 × 3 × 131

The distinct prime factors of 786 are 2, 3, 131. To factorize any other number, use the prime factorization calculator.

Factor tree of 786

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

Factor tree of 78678623933131
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 786

Number of factors8
Sum of factors1584
Sum of proper factors798
Prime factorization2 × 3 × 131
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 786 interesting

  • 786 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 786 is an abundant number: its proper factors sum to 798, which is 12 more than 786 itself.
  • 786 has 3 distinct prime factors (2, 3, 131), which is why it has so many divisors.

How to find the factors of 786 yourself

Divide 786 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 √786 ≈ 28.04, because every factor above that pairs with one below it.

786 ÷ 1 = 786 ✓
786 ÷ 2 = 393 ✓
786 ÷ 3 = 262 ✓
786 ÷ 6 = 131 ✓

Reading both columns gives every factor: 1, 2, 3, 6, 131, 262, 393, 786. The factor calculator does this automatically for any number.

Numbers mathematically connected to 786.

Frequently asked questions about 786

What are the factors of 786?

The factors of 786 are 1, 2, 3, 6, 131, 262, 393, and 786. That is 8 factors in total, counting both 1 and 786.

Is 786 a prime number?

No, 786 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 786 is also divisible by 2.

What is the prime factorization of 786?

The prime factorization of 786 is 2 × 3 × 131. Written out in full: 2 × 3 × 131 = 786. Its distinct prime factors are 2, 3, 131.

What two numbers multiply to give 786?

There are 4 pairs of whole numbers that multiply to 786: 1 × 786, 2 × 393, 3 × 262, 6 × 131.

What is the sum of the factors of 786?

Adding all the factors of 786 together gives 1584. Excluding 786 itself, the proper factors sum to 798.

Is 786 a perfect square?

No, 786 is not a perfect square. There is no whole number that multiplies by itself to give 786. The nearest perfect squares are 784 and 841.

What is the largest factor of 786 other than itself?

The largest factor of 786 apart from 786 itself is 393, since 786 ÷ 393 = 2.

How many factors does 786 have?

786 has 8 factors: 1, 2, 3, 6, 131, 262, 393, and 786. You can verify this from the prime factorization 2 × 3 × 131: add 1 to each exponent and multiply, giving 2 × 2 × 2 = 8.

Explore more

Try another number in the factor calculator, break 786 down further with the prime factorization calculator, or compare 786 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.