Factor Calculator

Factors of 66

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. In total, 66 has 8 factors. Its prime factorization is 2 × 3 × 11, and the sum of all its factors is 144.

All factors of 66

Here are all 8 factors of 66, listed from smallest to largest.

123611223366

Factor pairs of 66

These 4 pairs of whole numbers each multiply to give 66.

1 × 66 = 66
2 × 33 = 66
3 × 22 = 66
6 × 11 = 66

Prime factorization of 66

Dividing 66 by the smallest prime at each step gives its prime factorization:

66 ÷ 2 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
Result: 66 = 2 × 3 × 11 = 2 × 3 × 11

The distinct prime factors of 66 are 2, 3, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 66

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

Factor tree of 6666233311
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 66

Number of factors8
Sum of factors144
Sum of proper factors78
Prime factorization2 × 3 × 11
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 66 interesting

  • 66 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.
  • 66 is an abundant number: its proper factors sum to 78, which is 12 more than 66 itself.
  • 66 is a triangular number — it is the sum of the first 11 whole numbers (1 + 2 + … + 11 = 66).
  • 66 has 3 distinct prime factors (2, 3, 11), which is why it has so many divisors.

How to find the factors of 66 yourself

Divide 66 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 √66 ≈ 8.12, because every factor above that pairs with one below it.

66 ÷ 1 = 66 ✓
66 ÷ 2 = 33 ✓
66 ÷ 3 = 22 ✓
66 ÷ 6 = 11 ✓

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

Numbers mathematically connected to 66.

Frequently asked questions about 66

What are the factors of 66?

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. That is 8 factors in total, counting both 1 and 66.

Is 66 a prime number?

No, 66 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 66 is also divisible by 2.

What is the prime factorization of 66?

The prime factorization of 66 is 2 × 3 × 11. Written out in full: 2 × 3 × 11 = 66. Its distinct prime factors are 2, 3, 11.

What two numbers multiply to give 66?

There are 4 pairs of whole numbers that multiply to 66: 1 × 66, 2 × 33, 3 × 22, 6 × 11.

What is the sum of the factors of 66?

Adding all the factors of 66 together gives 144. Excluding 66 itself, the proper factors sum to 78.

Is 66 a perfect square?

No, 66 is not a perfect square. There is no whole number that multiplies by itself to give 66. The nearest perfect squares are 64 and 81.

What is the largest factor of 66 other than itself?

The largest factor of 66 apart from 66 itself is 33, since 66 ÷ 33 = 2.

How many factors does 66 have?

66 has 8 factors: 1, 2, 3, 6, 11, 22, 33, and 66. You can verify this from the prime factorization 2 × 3 × 11: add 1 to each exponent and multiply, giving 2 × 2 × 2 = 8.

Explore more

Try another number in the factor calculator, break 66 down further with the prime factorization calculator, or compare 66 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.