Factor Calculator

Factors of 688

The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, and 688. In total, 688 has 10 factors. Its prime factorization is 2⁴ × 43, and the sum of all its factors is 1364.

All factors of 688

Here are all 10 factors of 688, listed from smallest to largest.

1248164386172344688

Factor pairs of 688

These 5 pairs of whole numbers each multiply to give 688.

1 × 688 = 688
2 × 344 = 688
4 × 172 = 688
8 × 86 = 688
16 × 43 = 688

Prime factorization of 688

Dividing 688 by the smallest prime at each step gives its prime factorization:

688 ÷ 2 = 344
344 ÷ 2 = 172
172 ÷ 2 = 86
86 ÷ 2 = 43
43 ÷ 43 = 1
Result: 688 = 2 × 2 × 2 × 2 × 43 = 2⁴ × 43

The distinct prime factors of 688 are 2, 43. To factorize any other number, use the prime factorization calculator.

Factor tree of 688

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

Factor tree of 68868823442172286243
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 688

Number of factors10
Sum of factors1364
Sum of proper factors676
Prime factorization2⁴ × 43
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 688 interesting

  • 688 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
  • 688 is a deficient number: its proper factors sum to 676, which is 12 less than 688 itself.

How to find the factors of 688 yourself

Divide 688 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 √688 ≈ 26.23, because every factor above that pairs with one below it.

688 ÷ 1 = 688 ✓
688 ÷ 2 = 344 ✓
688 ÷ 4 = 172 ✓
688 ÷ 8 = 86 ✓
688 ÷ 16 = 43 ✓

Reading both columns gives every factor: 1, 2, 4, 8, 16, 43, 86, 172, 344, 688. The factor calculator does this automatically for any number.

Numbers mathematically connected to 688.

Frequently asked questions about 688

What are the factors of 688?

The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, and 688. That is 10 factors in total, counting both 1 and 688.

Is 688 a prime number?

No, 688 is not prime — it is a composite number with 10 factors. A prime number has exactly two factors, but 688 is also divisible by 2.

What is the prime factorization of 688?

The prime factorization of 688 is 2⁴ × 43. Written out in full: 2 × 2 × 2 × 2 × 43 = 688. Its distinct prime factors are 2, 43.

What two numbers multiply to give 688?

There are 5 pairs of whole numbers that multiply to 688: 1 × 688, 2 × 344, 4 × 172, 8 × 86, 16 × 43.

What is the sum of the factors of 688?

Adding all the factors of 688 together gives 1364. Excluding 688 itself, the proper factors sum to 676.

Is 688 a perfect square?

No, 688 is not a perfect square. There is no whole number that multiplies by itself to give 688. The nearest perfect squares are 676 and 729.

What is the largest factor of 688 other than itself?

The largest factor of 688 apart from 688 itself is 344, since 688 ÷ 344 = 2.

How many factors does 688 have?

688 has 10 factors: 1, 2, 4, 8, 16, 43, 86, 172, 344, and 688. You can verify this from the prime factorization 2⁴ × 43: add 1 to each exponent and multiply, giving 5 × 2 = 10.

Explore more

Try another number in the factor calculator, break 688 down further with the prime factorization calculator, or compare 688 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.