Divisors of 144: All 15 Factors
Quick Answer
144 has 15 divisors (factors): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Sum: 403. 144 is a perfect square (√144 = 12).
Divisors (Factors) Calculator
Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).
All Divisors of 144
The number 144 has 15 divisors:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Divisor Pairs of 144
Each pair multiplies to 144:
| Factor 1 | × | Factor 2 | = | 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 |
Note: the last pair has identical factors (12 × 12) because 144 is a perfect square.
Number of Divisors
The number 144 has 15 divisors, written as τ(144) = 15 in number theory.
⚡ Notice: 144 has an odd number of divisors — this means 144 is a perfect square (√144 = 12).
Sum of Divisors
σ(144) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 + 144 = 403
Prime Factorization of 144
Properties of 144
- 144 is composite.
- 144 is a perfect square (√144 = 12).
- Number of divisors: 15.
- Sum of divisors: 403.
Common Divisors with Another Number?
Looking for the divisors that 144 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.
Step-by-Step: How to Find the Divisors of 144
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √144 ≈ 12.00. If i divides 144, then both i and 144/i are divisors.
- 1 divides 144 (144 ÷ 1 = 144) → pair (1, 144)
- 2 divides 144 (144 ÷ 2 = 72) → pair (2, 72)
- 3 divides 144 (144 ÷ 3 = 48) → pair (3, 48)
- 4 divides 144 (144 ÷ 4 = 36) → pair (4, 36)
- 6 divides 144 (144 ÷ 6 = 24) → pair (6, 24)
- 8 divides 144 (144 ÷ 8 = 18) → pair (8, 18)
- 9 divides 144 (144 ÷ 9 = 16) → pair (9, 16)
- 12 divides 144 (144 ÷ 12 = 12) → pair (12, 12)
- Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144} — total 15 divisors.
- Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 + 144 = 403.
Nearby Examples
Related Operations for 144
- Multiples of 144 — "outward" complement; M is a multiple of 144 ⇔ 144 is a divisor of M
- 144 Prime Factorization — decompose into prime building blocks
- Find GCF of 144 and another number
- Find LCM of 144 and another number
- Is 144 a perfect square? (odd divisor count ⇔ yes)
See also our tables of divisors:
What Is a Divisor?
A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.
Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.
Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.
Divisors Calculation Examples
Find all divisors of these numbers:
Related Calculators
- Multiples of a Number — "outward" complement
- Prime Factorization — product of prime divisors
- Greatest Common Factor (GCF) — largest common divisor of 2+ numbers
- Least Common Multiple (LCM) — smallest common multiple
- Is N a Perfect Square? — odd divisor count check