Divisors of 40: All 8 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 40

The number 40 has 8 divisors:

1,  2,  4,  5,  8,  10,  20,  40

Divisor Pairs of 40

Each pair multiplies to 40:

Number of Divisors

The number 40 has 8 divisors, written as τ(40) = 8 in number theory.

Sum of Divisors

σ(40) = 1 + 2 + 4 + 5 + 8 + 10 + 20 + 40 = 90

Prime Factorization of 40

See the full prime factorization calculator →

Properties of 40

• 40 is composite.
• 40 is not a perfect square.
• Number of divisors: 8.
• Sum of divisors: 90.

Common Divisors with Another Number?

Looking for the divisors that 40 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 40

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √40 ≈ 6.32. If i divides 40, then both i and 40/i are divisors.

1. 1 divides 40 (40 ÷ 1 = 40) → pair (1, 40)
2. 2 divides 40 (40 ÷ 2 = 20) → pair (2, 20)
3. 4 divides 40 (40 ÷ 4 = 10) → pair (4, 10)
4. 5 divides 40 (40 ÷ 5 = 8) → pair (5, 8)
5. Collect all unique values: {1, 2, 4, 5, 8, 10, 20, 40} — total 8 divisors.
6. Sum: 1 + 2 + 4 + 5 + 8 + 10 + 20 + 40 = 90.

Nearby Examples

Related Operations for 40

• Multiples of 40 — "outward" complement; M is a multiple of 40 ⇔ 40 is a divisor of M
• 40 Prime Factorization — decompose into prime building blocks
• Find GCF of 40 and another number
• Find LCM of 40 and another number
• Is 40 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

Find all divisors of these numbers: