Divisors of 138: 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 138

The number 138 has 8 divisors:

1,  2,  3,  6,  23,  46,  69,  138

Divisor Pairs of 138

Each pair multiplies to 138:

Number of Divisors

The number 138 has 8 divisors, written as τ(138) = 8 in number theory.

Sum of Divisors

σ(138) = 1 + 2 + 3 + 6 + 23 + 46 + 69 + 138 = 288

Prime Factorization of 138

See the full prime factorization calculator →

Properties of 138

• 138 is composite.
• 138 is not a perfect square.
• Number of divisors: 8.
• Sum of divisors: 288.

Common Divisors with Another Number?

Looking for the divisors that 138 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 138

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √138 ≈ 11.75. If i divides 138, then both i and 138/i are divisors.

1. 1 divides 138 (138 ÷ 1 = 138) → pair (1, 138)
2. 2 divides 138 (138 ÷ 2 = 69) → pair (2, 69)
3. 3 divides 138 (138 ÷ 3 = 46) → pair (3, 46)
4. 6 divides 138 (138 ÷ 6 = 23) → pair (6, 23)
5. Collect all unique values: {1, 2, 3, 6, 23, 46, 69, 138} — total 8 divisors.
6. Sum: 1 + 2 + 3 + 6 + 23 + 46 + 69 + 138 = 288.

Nearby Examples

Related Operations for 138

• Multiples of 138 — "outward" complement; M is a multiple of 138 ⇔ 138 is a divisor of M
• 138 Prime Factorization — decompose into prime building blocks
• Find GCF of 138 and another number
• Find LCM of 138 and another number
• Is 138 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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