Factors are whole numbers that divide another number evenly. They help with simplification, grouping, divisibility, and understanding the structure of an integer.
Find factor pairs
For 36, start at 1 and test divisors through the square root. The pairs are 1×36, 2×18, 3×12, 4×9, and 6×6. Listing one side of each pair prevents duplicates.
Factors versus multiples
Factors divide a number; multiples are produced by multiplying it. Six is a factor of 36, while 36, 42, and 48 are multiples of 6. Mixing the terms can lead to incorrect fraction and GCF work.
Prime factorization
Break 36 into primes: 36 = 2 × 18 = 2 × 2 × 9 = 2² × 3². Prime factors provide a compact foundation for GCF, LCM, and divisibility reasoning.
Use the result carefully
Zero and one are special cases. Zero has infinitely many divisors in the usual integer sense, while one has only one positive factor and is neither prime nor composite.
Sources
The figures and rules in this guide are checked against:
- Divisor — Wolfram MathWorld
- Prime Factorization — Wolfram MathWorld
- Fundamental Theorem of Arithmetic — Wolfram MathWorld
- Factor (mathematics) — Encyclopaedia Britannica