Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 12/52,73/65,56/91,51/21
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 12,73,56,51
Greatest Common Factor of Numerators i.e. GCF of 12,73,56,51 is 1 .
LCM of Denominators means LCM of 52,65,91,21 as per the given fractions.
LCM of 52,65,91,21 is 5460 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 12,73,56,51
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 73
List of positive integer factors of 73 that divides 73 without a remainder.
1,73
Factors of 56
List of positive integer factors of 56 that divides 56 without a remainder.
1,2,4,7,8,14,28,56
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Greatest Common Factor
We found the factors 12,73,56,51 . The biggest common factor number is the GCF number.
So the greatest common factor 12,73,56,51 is 1.
Lets's calculate LCM of 52,65,91,21
7 | 52, 65, 91, 21 |
13 | 52, 65, 13, 3 |
4, 5, 1, 3 |
∴ So the LCM of the given numbers is 7 x 13 x 4 x 5 x 1 x 3 = 5460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5460
Therefore, the GCF of Fractions 12/52,73/65,56/91,51/21 is 1/5460
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 52,65,91,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,65,91,21) = 1
common factors(in case of two or more numbers have common factors) = 1183
GCF(52,65,91,21) x common factors =1 x 1183 = 1183
LCM(52,65,91,21) = ( 52 × 65 × 91 × 21 ) / 1183
LCM(52,65,91,21) = 6459180 / 1183
LCM(52,65,91,21) = 5460
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
2. What is the GCF of Fractions for 12/52, 73/65, 56/91, 51/21?
Answer: GCF of Numerators as per given numbers 12/52, 73/65, 56/91, 51/21 is
GCF of Numerators i.e. for 12,73,56,51 is 1
LCM of denominators i.e. for 52,65,91,21 is 5460.
Thus, GCF of Fractions is 1/5460.Finally, GCF of Fractions for 12/52, 73/65, 56/91, 51/21 is 1/5460.