The factors of 66 are the whole numbers that divide 66 exactly, leaving no remainder: 1, 2, 3, 6, 11, 22, 33, 66. Use the calculator above for any number, or read on for the factor pairs, prime factorization and properties of 66.
What are the factors of 66?
A factor of 66 is any whole number that divides 66 with no remainder. Listing them from smallest to largest, the factors of 66 are:
1, 2, 3, 6, 11, 22, 33, 66
So 66 is a composite number with 8 factors in total. Every number has 1 and itself as factors; the interesting work is finding the ones in between.
Factor pairs of 66
A factor pair is two numbers that multiply to give 66. The factor pairs of 66 are:
| Factor pair | Product |
|---|---|
| 1 × 66 | 66 |
| 2 × 33 | 66 |
| 3 × 22 | 66 |
| 6 × 11 | 66 |
Prime factorization of 66
The prime factorization breaks 66 down into a product of prime numbers only:
$$ 66 = 2 \times 3 \times 11 $$How to find the factors of 66, step by step
- Start at 1 — 1 divides every number, so 1 and 66 are always factors.
- Test each whole number from 2 upward: if it divides 66 exactly, it is a factor.
- Use factor pairs — each small factor gives a matching large factor, so you only need to test up to $\sqrt{66}$.
- List them in order to get all 8 factors of 66.
Factors versus multiples of 66
It is easy to mix these up. The factors of 66 are the numbers that divide into 66 (they are less than or equal to 66), while the multiples of 66 are what you get by multiplying 66 outward: 66, 132, 198, 264, and so on. In short: factors go in, multiples go out. 66 is an even number, and its smallest prime factor is 2.
Properties of 66
| Number of factors | 8 |
| Sum of factors | 144 |
| Sum of proper divisors | 78 |
| Prime or composite | Composite |
| Even or odd | Even |
| Perfect square | No |
| Prime factorization | 2 x 3 x 11 |
Is 66 abundant, deficient or perfect?
Number theorists classify a number by comparing it to the sum of its proper divisors (all its factors except itself). For 66, those proper divisors add up to 78, which makes 66 an abundant number (its proper divisors sum to 78, which is more than 66). Most numbers are deficient; abundant and perfect numbers are comparatively rare, which is what makes this property interesting.
Using the factors of 66 for GCF and LCM
The prime factorization $2 \times 3 \times 11$ is the shortcut for combining 66 with another number. To find the greatest common factor (GCF), take the primes 66 shares with the other number, each to the lowest power. For the least common multiple (LCM), take every prime that appears in either number, each to the highest power. This is why the prime factorization is worth writing down — it does the heavy lifting for fractions, ratios and simplification.
Related factors and tools
Explore more: Factors of 64 Factors of 63 Factors of 70. Or find the factors of any number with the Factor Calculator. Exponents are the reverse idea — see logarithms and read the formal reference on divisors at Wikipedia.