Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 58/14,72/71,43/76,51/132
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 58,72,43,51
Greatest Common Factor of Numerators i.e. GCF of 58,72,43,51 is 1 .
LCM of Denominators means LCM of 14,71,76,132 as per the given fractions.
LCM of 14,71,76,132 is 1246476 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 58,72,43,51
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 58
List of positive integer factors of 58 that divides 58 without a remainder.
1,2,29,58
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
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 58,72,43,51 . The biggest common factor number is the GCF number.
So the greatest common factor 58,72,43,51 is 1.
Lets's calculate LCM of 14,71,76,132
2 | 14, 71, 76, 132 |
2 | 7, 71, 38, 66 |
7, 71, 19, 33 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 71 x 19 x 33 = 1246476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1246476
Therefore, the GCF of Fractions 58/14,72/71,43/76,51/132 is 1/1246476
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 14,71,76,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,71,76,132) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(14,71,76,132) x common factors =1 x 8 = 8
LCM(14,71,76,132) = ( 14 × 71 × 76 × 132 ) / 8
LCM(14,71,76,132) = 9971808 / 8
LCM(14,71,76,132) = 1246476
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 58/14, 72/71, 43/76, 51/132?
Answer: GCF of Numerators as per given numbers 58/14, 72/71, 43/76, 51/132 is
GCF of Numerators i.e. for 58,72,43,51 is 1
LCM of denominators i.e. for 14,71,76,132 is 1246476.
Thus, GCF of Fractions is 1/1246476.Finally, GCF of Fractions for 58/14, 72/71, 43/76, 51/132 is 1/1246476.