Divisors of 35721: All 21 Factors

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 35721

The number 35721 has 21 divisors:

1,  3,  7,  9,  21,  27,  49,  63,  81,  147,  189,  243,  441,  567,  729,  1323,  1701,  3969,  5103,  11907,  35721

Divisor Pairs of 35721

Each pair multiplies to 35721:

Note: the last pair has identical factors (189 × 189) because 35721 is a perfect square.

Number of Divisors

The number 35721 has 21 divisors, written as τ(35721) = 21 in number theory.

⚡ Notice: 35721 has an odd number of divisors — this means 35721 is a perfect square (√35721 = 189).

Sum of Divisors

σ(35721) = 1 + 3 + 7 + 9 + 21 + 27 + 49 + 63 + 81 + 147 + 189 + 243 + 441 + 567 + 729 + 1323 + 1701 + 3969 + 5103 + 11907 + 35721 = 62301

Prime Factorization of 35721

See the full prime factorization calculator →

Properties of 35721

• 35721 is composite.
• 35721 is a perfect square (√35721 = 189).
• Number of divisors: 21.
• Sum of divisors: 62301.

Common Divisors with Another Number?

Looking for the divisors that 35721 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 35721

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √35721 ≈ 189.00. If i divides 35721, then both i and 35721/i are divisors.

1. 1 divides 35721 (35721 ÷ 1 = 35721) → pair (1, 35721)
2. 3 divides 35721 (35721 ÷ 3 = 11907) → pair (3, 11907)
3. 7 divides 35721 (35721 ÷ 7 = 5103) → pair (7, 5103)
4. 9 divides 35721 (35721 ÷ 9 = 3969) → pair (9, 3969)
5. 21 divides 35721 (35721 ÷ 21 = 1701) → pair (21, 1701)
6. 27 divides 35721 (35721 ÷ 27 = 1323) → pair (27, 1323)
7. 49 divides 35721 (35721 ÷ 49 = 729) → pair (49, 729)
8. 63 divides 35721 (35721 ÷ 63 = 567) → pair (63, 567)
9. 81 divides 35721 (35721 ÷ 81 = 441) → pair (81, 441)
10. 147 divides 35721 (35721 ÷ 147 = 243) → pair (147, 243)
11. 189 divides 35721 (35721 ÷ 189 = 189) → pair (189, 189)
12. Collect all unique values: {1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 243, 441, 567, 729, 1323, 1701, 3969, 5103, 11907, 35721} — total 21 divisors.
13. Sum: 1 + 3 + 7 + 9 + 21 + 27 + 49 + 63 + 81 + 147 + 189 + 243 + 441 + 567 + 729 + 1323 + 1701 + 3969 + 5103 + 11907 + 35721 = 62301.

Nearby Examples

Related Operations for 35721

• Multiples of a Number — "outward" complement of divisors
• 35721 Prime Factorization — decompose into prime building blocks
• Find GCF of 35721 and another number
• Find LCM of 35721 and another number
• Is 35721 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

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.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

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