Factor Calculator

Factors of 712

The factors of 712 are 1, 2, 4, 8, 89, 178, 356, and 712. In total, 712 has 8 factors. Its prime factorization is 2³ × 89, and the sum of all its factors is 1350.

All factors of 712

Here are all 8 factors of 712, listed from smallest to largest.

124889178356712

Factor pairs of 712

These 4 pairs of whole numbers each multiply to give 712.

1 × 712 = 712
2 × 356 = 712
4 × 178 = 712
8 × 89 = 712

Prime factorization of 712

Dividing 712 by the smallest prime at each step gives its prime factorization:

712 ÷ 2 = 356
356 ÷ 2 = 178
178 ÷ 2 = 89
89 ÷ 89 = 1
Result: 712 = 2 × 2 × 2 × 89 = 2³ × 89

The distinct prime factors of 712 are 2, 89. To factorize any other number, use the prime factorization calculator.

Factor tree of 712

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

Factor tree of 71271223562178289
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 712

Number of factors8
Sum of factors1350
Sum of proper factors638
Prime factorization2³ × 89
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 712 interesting

  • 712 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.
  • 712 is a deficient number: its proper factors sum to 638, which is 74 less than 712 itself.

How to find the factors of 712 yourself

Divide 712 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 √712 ≈ 26.68, because every factor above that pairs with one below it.

712 ÷ 1 = 712 ✓
712 ÷ 2 = 356 ✓
712 ÷ 4 = 178 ✓
712 ÷ 8 = 89 ✓

Reading both columns gives every factor: 1, 2, 4, 8, 89, 178, 356, 712. The factor calculator does this automatically for any number.

Numbers mathematically connected to 712.

Frequently asked questions about 712

What are the factors of 712?

The factors of 712 are 1, 2, 4, 8, 89, 178, 356, and 712. That is 8 factors in total, counting both 1 and 712.

Is 712 a prime number?

No, 712 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 712 is also divisible by 2.

What is the prime factorization of 712?

The prime factorization of 712 is 2³ × 89. Written out in full: 2 × 2 × 2 × 89 = 712. Its distinct prime factors are 2, 89.

What two numbers multiply to give 712?

There are 4 pairs of whole numbers that multiply to 712: 1 × 712, 2 × 356, 4 × 178, 8 × 89.

What is the sum of the factors of 712?

Adding all the factors of 712 together gives 1350. Excluding 712 itself, the proper factors sum to 638.

Is 712 a perfect square?

No, 712 is not a perfect square. There is no whole number that multiplies by itself to give 712. The nearest perfect squares are 676 and 729.

What is the largest factor of 712 other than itself?

The largest factor of 712 apart from 712 itself is 356, since 712 ÷ 356 = 2.

How many factors does 712 have?

712 has 8 factors: 1, 2, 4, 8, 89, 178, 356, and 712. You can verify this from the prime factorization 2³ × 89: add 1 to each exponent and multiply, giving 4 × 2 = 8.

Explore more

Try another number in the factor calculator, break 712 down further with the prime factorization calculator, or compare 712 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.