Find every whole number that divides all inputs evenly, including the GCF highlight.
Overview
Factoring underpins fraction simplification, divisibility puzzles, and number theory exercises. A common factor divides every number in a set without remainder. Listing them reveals structure that a single GCF value alone might hide.
To find common factors of 24 and 36, list factors of each: 1,2,3,4,6,8,12,24 and 1,2,3,4,6,9,12,18,36. The intersection is 1,2,3,4,6,12, with 12 greatest. This calculator automates that intersection.
For three numbers, intersect factor sets pairwise or compute GCF iteratively. Teachers use common factor lists to show why 12 is the largest shared divisor, not just the final answer from an algorithm.
When simplifying ratios or fractions with multiple denominators, the GCF of numerators and denominators after combining terms keeps expressions minimal and easier to communicate.
Steps
Provide two or more whole numbers.
Compute divisors for each input.
Keep divisors shared by all numbers.
Identify the largest shared factor.
Divide numerator and denominator by GCF.
Copy the list for homework or reports.
Math
Common factors = Factors(n1) ∩ Factors(n2) ∩ ...; GCF = max(common factors)
Divisors are tested up to sqrt(n) for efficiency. Shared divisors form the intersection; the maximum element is the GCF.
Worked cases
Intersect {1,2,3,4,6,8,12,24} and {1,2,3,4,6,9,12,18,36}
1,2,3,4,6,12 with GCF 12.
Only shared divisor is 1
Common factor list: 1.
Shared divisors include 1,3,5,15
GCF = 15.
Why use this
Questions