Explain how to find the greatest common factor of three numbers.
Grade 6 GO MATH BOOK
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To find the greatest common factor (GCF) of three numbers, you can follow these steps:
Step 1: Determine the prime factors of each number.
Start by finding the prime factors of each number. Prime factors are the prime numbers that multiply together to form a given number.
For example, let's say we have three numbers: 24, 36, and 48.
The prime factors of 24 are 2 x 2 x 2 x 3, which can be written as 2^3 x 3.
The prime factors of 36 are 2 x 2 x 3 x 3, which can be written as 2^2 x 3^2.
The prime factors of 48 are 2 x 2 x 2 x 2 x 3, which can be written as 2^4 x 3.
Step 2: Identify the common prime factors.
Look for the prime factors that are common among all three numbers. These common factors will be the ones that appear in the prime factorization of all three numbers.
In our example, the common prime factors are 2 and 3, as they appear in the prime factorization of all three numbers.
Step 3: Determine the GCF by multiplying the common prime factors.
To find the GCF, simply multiply the common prime factors together. If there are no common factors, the GCF would be 1.
In our example, the GCF of 24, 36, and 48 is 2 x 3, which equals 6.
So, the greatest common factor of 24, 36, and 48 is 6.