Divisors of 21025: All 9 Factors
Quick Answer
21025 has 9 divisors (factors): 1, 5, 25, 29, 145, 725, 841, 4205, 21025.
Sum: 27001. 21025 is a perfect square (√21025 = 145).
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 21025
The number 21025 has 9 divisors:
1, 5, 25, 29, 145, 725, 841, 4205, 21025
Divisor Pairs of 21025
Each pair multiplies to 21025:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 21025 | = | 21025 |
| 5 | × | 4205 | = | 21025 |
| 25 | × | 841 | = | 21025 |
| 29 | × | 725 | = | 21025 |
| 145 | × | 145 | = | 21025 |
Note: the last pair has identical factors (145 × 145) because 21025 is a perfect square.
Number of Divisors
The number 21025 has 9 divisors, written as τ(21025) = 9 in number theory.
⚡ Notice: 21025 has an odd number of divisors — this means 21025 is a perfect square (√21025 = 145).
Sum of Divisors
σ(21025) = 1 + 5 + 25 + 29 + 145 + 725 + 841 + 4205 + 21025 = 27001
Prime Factorization of 21025
Properties of 21025
- 21025 is composite.
- 21025 is a perfect square (√21025 = 145).
- Number of divisors: 9.
- Sum of divisors: 27001.
Common Divisors with Another Number?
Looking for the divisors that 21025 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 21025
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √21025 ≈ 145.00. If i divides 21025, then both i and 21025/i are divisors.
- 1 divides 21025 (21025 ÷ 1 = 21025) → pair (1, 21025)
- 5 divides 21025 (21025 ÷ 5 = 4205) → pair (5, 4205)
- 25 divides 21025 (21025 ÷ 25 = 841) → pair (25, 841)
- 29 divides 21025 (21025 ÷ 29 = 725) → pair (29, 725)
- 145 divides 21025 (21025 ÷ 145 = 145) → pair (145, 145)
- Collect all unique values: {1, 5, 25, 29, 145, 725, 841, 4205, 21025} — total 9 divisors.
- Sum: 1 + 5 + 25 + 29 + 145 + 725 + 841 + 4205 + 21025 = 27001.
Nearby Examples
Related Operations for 21025
- Multiples of a Number — "outward" complement of divisors
- 21025 Prime Factorization — decompose into prime building blocks
- Find GCF of 21025 and another number
- Find LCM of 21025 and another number
- Is 21025 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