Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 62/17,60/28,82/41,74/12
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 62,60,82,74
Greatest Common Factor of Numerators i.e. GCF of 62,60,82,74 is 2 .
LCM of Denominators means LCM of 17,28,41,12 as per the given fractions.
LCM of 17,28,41,12 is 58548 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 62,60,82,74
2 | 62, 60, 82, 74 |
31, 30, 41, 37 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 62
List of positive integer factors of 62 that divides 62 without a remainder.
1,2,31,62
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 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Greatest Common Factor
We found the factors 62,60,82,74 . The biggest common factor number is the GCF number.
So the greatest common factor 62,60,82,74 is 2.
Lets's calculate LCM of 17,28,41,12
2 | 17, 28, 41, 12 |
2 | 17, 14, 41, 6 |
17, 7, 41, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 17 x 7 x 41 x 3 = 58548
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/58548
Therefore, the GCF of Fractions 62/17,60/28,82/41,74/12 is 2/58548
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 17,28,41,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,28,41,12) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(17,28,41,12) x common factors =1 x 4 = 4
LCM(17,28,41,12) = ( 17 × 28 × 41 × 12 ) / 4
LCM(17,28,41,12) = 234192 / 4
LCM(17,28,41,12) = 58548
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 62/17, 60/28, 82/41, 74/12?
Answer: GCF of Numerators as per given numbers 62/17, 60/28, 82/41, 74/12 is
GCF of Numerators i.e. for 62,60,82,74 is 2
LCM of denominators i.e. for 17,28,41,12 is 58548.
Thus, GCF of Fractions is 2/58548.Finally, GCF of Fractions for 62/17, 60/28, 82/41, 74/12 is 2/58548.