Divisors of 1521: All 9 Factors
Quick Answer
1521 has 9 divisors (factors): 1, 3, 9, 13, 39, 117, 169, 507, 1521.
Sum: 2379. 1521 is a perfect square (√1521 = 39).
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 1521
The number 1521 has 9 divisors:
1, 3, 9, 13, 39, 117, 169, 507, 1521
Divisor Pairs of 1521
Each pair multiplies to 1521:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 1521 | = | 1521 |
| 3 | × | 507 | = | 1521 |
| 9 | × | 169 | = | 1521 |
| 13 | × | 117 | = | 1521 |
| 39 | × | 39 | = | 1521 |
Note: the last pair has identical factors (39 × 39) because 1521 is a perfect square.
Number of Divisors
The number 1521 has 9 divisors, written as τ(1521) = 9 in number theory.
⚡ Notice: 1521 has an odd number of divisors — this means 1521 is a perfect square (√1521 = 39).
Sum of Divisors
σ(1521) = 1 + 3 + 9 + 13 + 39 + 117 + 169 + 507 + 1521 = 2379
Prime Factorization of 1521
Properties of 1521
- 1521 is composite.
- 1521 is a perfect square (√1521 = 39).
- Number of divisors: 9.
- Sum of divisors: 2379.
Common Divisors with Another Number?
Looking for the divisors that 1521 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 1521
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √1521 ≈ 39.00. If i divides 1521, then both i and 1521/i are divisors.
- 1 divides 1521 (1521 ÷ 1 = 1521) → pair (1, 1521)
- 3 divides 1521 (1521 ÷ 3 = 507) → pair (3, 507)
- 9 divides 1521 (1521 ÷ 9 = 169) → pair (9, 169)
- 13 divides 1521 (1521 ÷ 13 = 117) → pair (13, 117)
- 39 divides 1521 (1521 ÷ 39 = 39) → pair (39, 39)
- Collect all unique values: {1, 3, 9, 13, 39, 117, 169, 507, 1521} — total 9 divisors.
- Sum: 1 + 3 + 9 + 13 + 39 + 117 + 169 + 507 + 1521 = 2379.
Nearby Examples
Related Operations for 1521
- Multiples of 1521 — "outward" complement; M is a multiple of 1521 ⇔ 1521 is a divisor of M
- 1521 Prime Factorization — decompose into prime building blocks
- Find GCF of 1521 and another number
- Find LCM of 1521 and another number
- Is 1521 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