Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 60/40,42/55,67/71,99/242
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 60,42,67,99
Greatest Common Factor of Numerators i.e. GCF of 60,42,67,99 is 1 .
LCM of Denominators means LCM of 40,55,71,242 as per the given fractions.
LCM of 40,55,71,242 is 343640 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 60,42,67,99
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Greatest Common Factor
We found the factors 60,42,67,99 . The biggest common factor number is the GCF number.
So the greatest common factor 60,42,67,99 is 1.
Lets's calculate LCM of 40,55,71,242
2 | 40, 55, 71, 242 |
5 | 20, 55, 71, 121 |
11 | 4, 11, 71, 121 |
4, 1, 71, 11 |
∴ So the LCM of the given numbers is 2 x 5 x 11 x 4 x 1 x 71 x 11 = 343640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/343640
Therefore, the GCF of Fractions 60/40,42/55,67/71,99/242 is 1/343640
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 40,55,71,242 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,55,71,242) = 1
common factors(in case of two or more numbers have common factors) = 110
GCF(40,55,71,242) x common factors =1 x 110 = 110
LCM(40,55,71,242) = ( 40 × 55 × 71 × 242 ) / 110
LCM(40,55,71,242) = 37800400 / 110
LCM(40,55,71,242) = 343640
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 60/40, 42/55, 67/71, 99/242?
Answer: GCF of Numerators as per given numbers 60/40, 42/55, 67/71, 99/242 is
GCF of Numerators i.e. for 60,42,67,99 is 1
LCM of denominators i.e. for 40,55,71,242 is 343640.
Thus, GCF of Fractions is 1/343640.Finally, GCF of Fractions for 60/40, 42/55, 67/71, 99/242 is 1/343640.