Factor Calculator

Factors of 693

The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, and 693. In total, 693 has 12 factors. Its prime factorization is 3² × 7 × 11, and the sum of all its factors is 1248.

All factors of 693

Here are all 12 factors of 693, listed from smallest to largest.

1379112133637799231693

Factor pairs of 693

These 6 pairs of whole numbers each multiply to give 693.

1 × 693 = 693
3 × 231 = 693
7 × 99 = 693
9 × 77 = 693
11 × 63 = 693
21 × 33 = 693

Prime factorization of 693

Dividing 693 by the smallest prime at each step gives its prime factorization:

693 ÷ 3 = 231
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
Result: 693 = 3 × 3 × 7 × 11 = 3² × 7 × 11

The distinct prime factors of 693 are 3, 7, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 693

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

Factor tree of 6936933231377711
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 693

Number of factors12
Sum of factors1248
Sum of proper factors555
Prime factorization3² × 7 × 11
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 693 interesting

  • 693 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.
  • 693 is a deficient number: its proper factors sum to 555, which is 138 less than 693 itself.
  • 693 has 3 distinct prime factors (3, 7, 11), which is why it has so many divisors.

How to find the factors of 693 yourself

Divide 693 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 √693 ≈ 26.32, because every factor above that pairs with one below it.

693 ÷ 1 = 693 ✓
693 ÷ 3 = 231 ✓
693 ÷ 7 = 99 ✓
693 ÷ 9 = 77 ✓
693 ÷ 11 = 63 ✓
693 ÷ 21 = 33 ✓

Reading both columns gives every factor: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693. The factor calculator does this automatically for any number.

Numbers mathematically connected to 693.

Frequently asked questions about 693

What are the factors of 693?

The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, and 693. That is 12 factors in total, counting both 1 and 693.

Is 693 a prime number?

No, 693 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 693 is also divisible by 3.

What is the prime factorization of 693?

The prime factorization of 693 is 3² × 7 × 11. Written out in full: 3 × 3 × 7 × 11 = 693. Its distinct prime factors are 3, 7, 11.

What two numbers multiply to give 693?

There are 6 pairs of whole numbers that multiply to 693: 1 × 693, 3 × 231, 7 × 99, 9 × 77, 11 × 63, 21 × 33.

What is the sum of the factors of 693?

Adding all the factors of 693 together gives 1248. Excluding 693 itself, the proper factors sum to 555.

Is 693 a perfect square?

No, 693 is not a perfect square. There is no whole number that multiplies by itself to give 693. The nearest perfect squares are 676 and 729.

What is the largest factor of 693 other than itself?

The largest factor of 693 apart from 693 itself is 231, since 693 ÷ 231 = 3.

How many factors does 693 have?

693 has 12 factors: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, and 693. You can verify this from the prime factorization 3² × 7 × 11: add 1 to each exponent and multiply, giving 3 × 2 × 2 = 12.

Explore more

Try another number in the factor calculator, break 693 down further with the prime factorization calculator, or compare 693 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.