The factors of 21 are the whole numbers that divide 21 exactly, leaving no remainder: 1, 3, 7, 21. Use the calculator above for any number, or read on for the factor pairs, prime factorization and properties of 21.
What are the factors of 21?
A factor of 21 is any whole number that divides 21 with no remainder. Listing them from smallest to largest, the factors of 21 are:
1, 3, 7, 21
So 21 is a composite number with 4 factors in total. Every number has 1 and itself as factors; the interesting work is finding the ones in between.
Factor pairs of 21
A factor pair is two numbers that multiply to give 21. The factor pairs of 21 are:
| Factor pair | Product |
|---|---|
| 1 × 21 | 21 |
| 3 × 7 | 21 |
Prime factorization of 21
The prime factorization breaks 21 down into a product of prime numbers only:
$$ 21 = 3 \times 7 $$How to find the factors of 21, step by step
- Start at 1 — 1 divides every number, so 1 and 21 are always factors.
- Test each whole number from 2 upward: if it divides 21 exactly, it is a factor.
- Use factor pairs — each small factor gives a matching large factor, so you only need to test up to $\sqrt{21}$.
- List them in order to get all 4 factors of 21.
Factors versus multiples of 21
It is easy to mix these up. The factors of 21 are the numbers that divide into 21 (they are less than or equal to 21), while the multiples of 21 are what you get by multiplying 21 outward: 21, 42, 63, 84, and so on. In short: factors go in, multiples go out. 21 is an odd number, and its smallest prime factor is 3.
Properties of 21
| Number of factors | 4 |
| Sum of factors | 32 |
| Sum of proper divisors | 11 |
| Prime or composite | Composite |
| Even or odd | Odd |
| Perfect square | No |
| Prime factorization | 3 x 7 |
Is 21 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 21, those proper divisors add up to 11, which makes 21 a deficient number (its proper divisors sum to 11, which is less than 21). Most numbers are deficient; abundant and perfect numbers are comparatively rare, which is what makes this property interesting.
Using the factors of 21 for GCF and LCM
The prime factorization $3 \times 7$ is the shortcut for combining 21 with another number. To find the greatest common factor (GCF), take the primes 21 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 20 Factors of 24 Factors of 18. 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.