greatest common factor (GCF)
The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest number that divides evenly into two or more integers
The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest number that divides evenly into two or more integers. It is used to simplify fractions, factor polynomials, and solve various math problems.
To find the GCF of two numbers, you can use either of the following methods: prime factorization or division.
Method 1: Prime Factorization
1. Start by finding the prime factors of both numbers.
2. Multiply the common prime factors, using the lowest exponent for each factor.
3. The product obtained will be the GCF of the two numbers.
Example:
Let’s find the GCF of 36 and 48.
Step 1: Prime factorization of 36 = 2^2 * 3^2
Prime factorization of 48 = 2^4 * 3^1
Step 2: Multiply the common prime factors:
GCF = 2^2 * 3^1 = 12
So, the GCF of 36 and 48 is 12.
Method 2: Division
1. Divide the larger number by the smaller number.
2. Divide the remainder obtained from the previous step by the smaller number.
3. Repeat the division process until the remainder is zero.
4. The divisor from the last division step will be the GCF of the two numbers.
Example:
Let’s find the GCF of 54 and 72 using division.
Step 1: Divide 72 by 54: 72 ÷ 54 = 1 remainder 18
Step 2: Divide 54 by 18: 54 ÷ 18 = 3 remainder 0
Since the remainder is zero, the divisor from the last division (18) is the GCF of 54 and 72.
So, the GCF of 54 and 72 is 18.
Both methods will provide the same GCF, but you can choose the method that you find more comfortable or suitable for the given numbers.
More Answers:
Understanding Ordered Pairs: The Essentials of Coordinate Plane and Mathematical RelationshipsUnderstanding and Utilizing the Coordinate Plane in Mathematics: A Comprehensive Guide
Essential Formulas for Calculating Volume of Common Geometric Shapes