Divisors of 112: All 10 Factors
Quick Answer
112 has 10 divisors (factors): 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
Sum: 248.
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 112
The number 112 has 10 divisors:
1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Divisor Pairs of 112
Each pair multiplies to 112:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 112 | = | 112 |
| 2 | × | 56 | = | 112 |
| 4 | × | 28 | = | 112 |
| 7 | × | 16 | = | 112 |
| 8 | × | 14 | = | 112 |
Number of Divisors
The number 112 has 10 divisors, written as τ(112) = 10 in number theory.
Sum of Divisors
σ(112) = 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 56 + 112 = 248
Prime Factorization of 112
Properties of 112
- 112 is composite.
- 112 is not a perfect square.
- Number of divisors: 10.
- Sum of divisors: 248.
Common Divisors with Another Number?
Looking for the divisors that 112 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 112
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √112 ≈ 10.58. If i divides 112, then both i and 112/i are divisors.
- 1 divides 112 (112 ÷ 1 = 112) → pair (1, 112)
- 2 divides 112 (112 ÷ 2 = 56) → pair (2, 56)
- 4 divides 112 (112 ÷ 4 = 28) → pair (4, 28)
- 7 divides 112 (112 ÷ 7 = 16) → pair (7, 16)
- 8 divides 112 (112 ÷ 8 = 14) → pair (8, 14)
- Collect all unique values: {1, 2, 4, 7, 8, 14, 16, 28, 56, 112} — total 10 divisors.
- Sum: 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 56 + 112 = 248.
Nearby Examples
Related Operations for 112
- Multiples of 112 — "outward" complement; M is a multiple of 112 ⇔ 112 is a divisor of M
- 112 Prime Factorization — decompose into prime building blocks
- Find GCF of 112 and another number
- Find LCM of 112 and another number
- Is 112 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