The factors of 144 are the whole numbers that divide 144 exactly, leaving no remainder: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Use the calculator above for any number, or read on for the factor pairs, prime factorization and properties of 144.
What are the factors of 144?
A factor of 144 is any whole number that divides 144 with no remainder. Listing them from smallest to largest, the factors of 144 are:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
So 144 is a composite number with 15 factors in total. Every number has 1 and itself as factors; the interesting work is finding the ones in between.
Factor pairs of 144
A factor pair is two numbers that multiply to give 144. The factor pairs of 144 are:
| Factor pair | Product |
|---|---|
| 1 × 144 | 144 |
| 2 × 72 | 144 |
| 3 × 48 | 144 |
| 4 × 36 | 144 |
| 6 × 24 | 144 |
| 8 × 18 | 144 |
| 9 × 16 | 144 |
| 12 × 12 | 144 |
Prime factorization of 144
The prime factorization breaks 144 down into a product of prime numbers only:
$$ 144 = 2^{4} \times 3^{2} $$How to find the factors of 144, step by step
- Start at 1 — 1 divides every number, so 1 and 144 are always factors.
- Test each whole number from 2 upward: if it divides 144 exactly, it is a factor.
- Use factor pairs — each small factor gives a matching large factor, so you only need to test up to $\sqrt{144}$.
- List them in order to get all 15 factors of 144.
Factors versus multiples of 144
It is easy to mix these up. The factors of 144 are the numbers that divide into 144 (they are less than or equal to 144), while the multiples of 144 are what you get by multiplying 144 outward: 144, 288, 432, 576, and so on. In short: factors go in, multiples go out. 144 is an even number, and its smallest prime factor is 2.
Properties of 144
| Number of factors | 15 |
| Sum of factors | 403 |
| Sum of proper divisors | 259 |
| Prime or composite | Composite |
| Even or odd | Even |
| Perfect square | Yes |
| Prime factorization | 2^4 x 3^2 |
Is 144 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 144, those proper divisors add up to 259, which makes 144 an abundant number (its proper divisors sum to 259, which is more than 144). Most numbers are deficient; abundant and perfect numbers are comparatively rare, which is what makes this property interesting.
Using the factors of 144 for GCF and LCM
The prime factorization $2^{4} \times 3^{2}$ is the shortcut for combining 144 with another number. To find the greatest common factor (GCF), take the primes 144 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 120 Factors of 108 Factors of 100. 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.