Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/74,30/77,25/99,122/35
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 36,30,25,122
Greatest Common Factor of Numerators i.e. GCF of 36,30,25,122 is 1 .
LCM of Denominators means LCM of 74,77,99,35 as per the given fractions.
LCM of 74,77,99,35 is 256410 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 36,30,25,122
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Factors of 122
List of positive integer factors of 122 that divides 122 without a remainder.
1,2,61,122
Greatest Common Factor
We found the factors 36,30,25,122 . The biggest common factor number is the GCF number.
So the greatest common factor 36,30,25,122 is 1.
Lets's calculate LCM of 74,77,99,35
7 | 74, 77, 99, 35 |
11 | 74, 11, 99, 5 |
74, 1, 9, 5 |
∴ So the LCM of the given numbers is 7 x 11 x 74 x 1 x 9 x 5 = 256410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/256410
Therefore, the GCF of Fractions 36/74,30/77,25/99,122/35 is 1/256410
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 74,77,99,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,77,99,35) = 1
common factors(in case of two or more numbers have common factors) = 77
GCF(74,77,99,35) x common factors =1 x 77 = 77
LCM(74,77,99,35) = ( 74 × 77 × 99 × 35 ) / 77
LCM(74,77,99,35) = 19743570 / 77
LCM(74,77,99,35) = 256410
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 36/74, 30/77, 25/99, 122/35?
Answer: GCF of Numerators as per given numbers 36/74, 30/77, 25/99, 122/35 is
GCF of Numerators i.e. for 36,30,25,122 is 1
LCM of denominators i.e. for 74,77,99,35 is 256410.
Thus, GCF of Fractions is 1/256410.Finally, GCF of Fractions for 36/74, 30/77, 25/99, 122/35 is 1/256410.