Rules to find GCF :
(1) Factor method: follow the steps given below:
Step1: find all the factors of given numbers. (To know how to find factors, Click here.)
Example: suppose we need to find GCF of 12 and 16.
Step1: Factors of \(12=1,\ 2,\ 3,\ 4,\ 6,\ 12\)
Factors of \(16=1,\ 2,\ 4,\ 8,\ 16\)
Step 2: GCF = 4
:
Note: This
method is best for smaller numbers. See the other two methods below:
(2) Prime factorization method: follow the steps given below:
Step1: find all the prime factors of given numbers. (To know how to find prime factors, Click here.)
Step 2: identify the common factors.
Step 3: find the product of all the common factors.
Step 4: the product is the GCF of all the given numbers.
Example: suppose we need to find GCF of 24 and 81.
Step1: Prime factors of \(24=2\times2\times2\times3\)
Prime factors of \(18=2\times3\times3\)
Step 2: Common factors = 2 and 3
Step 3: product of common factors \(=2\times3=6\)
Step4: GCF of 24 and 18=6
(3) Exponent method: follow the following steps:
Step1: find all the prime factors of given numbers. (To know how to find prime factors, Click here.)
Step 2: write all the factors in exponential form. (To know about exponential form, click here)
Step 3: find the product of all the common factors with lowest exponent.
Step 4: the product is the GCF of all the given numbers.
Example: suppose we need to find GCF of 24 and 81.
Step 1 and 2: Prime factors of \(24=2\times2\times2\times3\)
Prime Factors of 24 in exponential form \(=2^3\times3^1\)
Prime factors of \(18=2\times3\times3\)
Prime Factors of 18 in exponential form \(=2^1\times3^2\)
Step 3: product of common factors with lowest exponent \(={2^1\times3}^1\)
\(=2\times3=6\)
Step4: GCF of 24 and 18=6
Another example: find GCF of 24, 36 and 54
Prime factorization rule: (To know how to find prime factors, Click here.)
Step1: Prime factors of \(24=2\times2\times2\times3\)
Prime factors of \(36=2\times2\times3\times3\)
Prime factors of \(108=2\times2\times3\times3\times3\)
Step 2: Common factors = 2, 2 and 3
Step 3: product of common factors \(=2\times2\times3=12\)
Step4: GCF of 24, 36 and 108=12
Exponent rule: (To know about exponents and exponential form, click here)
Step 1 and 2: Prime factors of \(24=2\times2\times2\times3\)
Prime Factors of 24 in exponential form \(=2^3\times3^1\)
Prime factors of \(36=2\times2\times3\times3\)
Prime Factors of 36 in exponential form \(=2^3\times3^1\)
Prime factors of \(108=2\times2\times3\times3\times3\)
Prime Factors of 108 in exponential form \(=2^2\times3^3\)
Step 3: product of common factors with lowest exponent \(={2^2\times3}^1\)
\(=2\times2\times3=12\)
Step4: GCF of 24, 36 and 108=12