Factor Calculator

Factors of 726

The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726. In total, 726 has 12 factors. Its prime factorization is 2 × 3 × 11², and the sum of all its factors is 1596.

All factors of 726

Here are all 12 factors of 726, listed from smallest to largest.

123611223366121242363726

Factor pairs of 726

These 6 pairs of whole numbers each multiply to give 726.

1 × 726 = 726
2 × 363 = 726
3 × 242 = 726
6 × 121 = 726
11 × 66 = 726
22 × 33 = 726

Prime factorization of 726

Dividing 726 by the smallest prime at each step gives its prime factorization:

726 ÷ 2 = 363
363 ÷ 3 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
Result: 726 = 2 × 3 × 11 × 11 = 2 × 3 × 11²

The distinct prime factors of 726 are 2, 3, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 726

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

Factor tree of 726726236331211111
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 726

Number of factors12
Sum of factors1596
Sum of proper factors870
Prime factorization2 × 3 × 11²
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 726 interesting

  • 726 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.
  • 726 is an abundant number: its proper factors sum to 870, which is 144 more than 726 itself.
  • 726 has 3 distinct prime factors (2, 3, 11), which is why it has so many divisors.

How to find the factors of 726 yourself

Divide 726 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 √726 ≈ 26.94, because every factor above that pairs with one below it.

726 ÷ 1 = 726 ✓
726 ÷ 2 = 363 ✓
726 ÷ 3 = 242 ✓
726 ÷ 6 = 121 ✓
726 ÷ 11 = 66 ✓
726 ÷ 22 = 33 ✓

Reading both columns gives every factor: 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726. The factor calculator does this automatically for any number.

Numbers mathematically connected to 726.

Frequently asked questions about 726

What are the factors of 726?

The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726. That is 12 factors in total, counting both 1 and 726.

Is 726 a prime number?

No, 726 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 726 is also divisible by 2.

What is the prime factorization of 726?

The prime factorization of 726 is 2 × 3 × 11². Written out in full: 2 × 3 × 11 × 11 = 726. Its distinct prime factors are 2, 3, 11.

What two numbers multiply to give 726?

There are 6 pairs of whole numbers that multiply to 726: 1 × 726, 2 × 363, 3 × 242, 6 × 121, 11 × 66, 22 × 33.

What is the sum of the factors of 726?

Adding all the factors of 726 together gives 1596. Excluding 726 itself, the proper factors sum to 870.

Is 726 a perfect square?

No, 726 is not a perfect square. There is no whole number that multiplies by itself to give 726. The nearest perfect squares are 676 and 729.

What is the largest factor of 726 other than itself?

The largest factor of 726 apart from 726 itself is 363, since 726 ÷ 363 = 2.

How many factors does 726 have?

726 has 12 factors: 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726. You can verify this from the prime factorization 2 × 3 × 11²: add 1 to each exponent and multiply, giving 2 × 2 × 3 = 12.

Explore more

Try another number in the factor calculator, break 726 down further with the prime factorization calculator, or compare 726 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.