The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more integers without leaving a remainder. In other words, it is the biggest number that is a factor of all the given numbers
Explanation:
- First, find all the factors of each number.
- Identify the factors that are common to all the numbers.
- The greatest common factor is the largest number among these common factors
Example:
For the numbers 12 and 30:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors: 1, 2, 3, 6
- Greatest common factor: 6
This means 6 is the largest number that divides both 12 and 30 exactly
Uses:
The GCF is useful for simplifying fractions, as dividing the numerator and denominator by their GCF reduces the fraction to its simplest form
Methods to find GCF:
- Listing factors and choosing the largest common one.
- Prime factorization: multiply the common prime factors.
- Euclidean algorithm: an efficient method using repeated division
In summary, the greatest common factor is the largest number that evenly divides two or more integers, helping in simplification and problem-solving involving divisibility
