Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 72/54,76/94,89/87,26/27
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 72,76,89,26
Greatest Common Factor of Numerators i.e. GCF of 72,76,89,26 is 1 .
LCM of Denominators means LCM of 54,94,87,27 as per the given fractions.
LCM of 54,94,87,27 is 73602 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 72,76,89,26
∴ So GCF of numbers is 1 because of no common factors present between them.
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 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Factors of 26
List of positive integer factors of 26 that divides 26 without a remainder.
1,2,13,26
Greatest Common Factor
We found the factors 72,76,89,26 . The biggest common factor number is the GCF number.
So the greatest common factor 72,76,89,26 is 1.
Lets's calculate LCM of 54,94,87,27
2 | 54, 94, 87, 27 |
3 | 27, 47, 87, 27 |
3 | 9, 47, 29, 9 |
3 | 3, 47, 29, 3 |
1, 47, 29, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 1 x 47 x 29 x 1 = 73602
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/73602
Therefore, the GCF of Fractions 72/54,76/94,89/87,26/27 is 1/73602
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 54,94,87,27 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,94,87,27) = 1
common factors(in case of two or more numbers have common factors) = 162
GCF(54,94,87,27) x common factors =1 x 162 = 162
LCM(54,94,87,27) = ( 54 × 94 × 87 × 27 ) / 162
LCM(54,94,87,27) = 11923524 / 162
LCM(54,94,87,27) = 73602
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 72/54, 76/94, 89/87, 26/27?
Answer: GCF of Numerators as per given numbers 72/54, 76/94, 89/87, 26/27 is
GCF of Numerators i.e. for 72,76,89,26 is 1
LCM of denominators i.e. for 54,94,87,27 is 73602.
Thus, GCF of Fractions is 1/73602.Finally, GCF of Fractions for 72/54, 76/94, 89/87, 26/27 is 1/73602.