Divisors of 42: All 8 Factors
Quick Answer
42 has 8 divisors (factors): 1, 2, 3, 6, 7, 14, 21, 42.
Sum: 96.
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 42
The number 42 has 8 divisors:
1, 2, 3, 6, 7, 14, 21, 42
Divisor Pairs of 42
Each pair multiplies to 42:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 42 | = | 42 |
| 2 | × | 21 | = | 42 |
| 3 | × | 14 | = | 42 |
| 6 | × | 7 | = | 42 |
Number of Divisors
The number 42 has 8 divisors, written as τ(42) = 8 in number theory.
Sum of Divisors
σ(42) = 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 = 96
Prime Factorization of 42
Properties of 42
- 42 is composite.
- 42 is not a perfect square.
- Number of divisors: 8.
- Sum of divisors: 96.
Common Divisors with Another Number?
Looking for the divisors that 42 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 42
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √42 ≈ 6.48. If i divides 42, then both i and 42/i are divisors.
- 1 divides 42 (42 ÷ 1 = 42) → pair (1, 42)
- 2 divides 42 (42 ÷ 2 = 21) → pair (2, 21)
- 3 divides 42 (42 ÷ 3 = 14) → pair (3, 14)
- 6 divides 42 (42 ÷ 6 = 7) → pair (6, 7)
- Collect all unique values: {1, 2, 3, 6, 7, 14, 21, 42} — total 8 divisors.
- Sum: 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 = 96.
Related Operations for 42
- Multiples of 42 — "outward" complement; M is a multiple of 42 ⇔ 42 is a divisor of M
- 42 Prime Factorization — decompose into prime building blocks
- Find GCF of 42 and another number
- Find LCM of 42 and another number
- Is 42 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
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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