Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 522/36,354/51,728/77
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 522,354,728
Greatest Common Factor of Numerators i.e. GCF of 522,354,728 is 2 .
LCM of Denominators means LCM of 36,51,77 as per the given fractions.
LCM of 36,51,77 is 47124 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 522,354,728
2 | 522, 354, 728 |
261, 177, 364 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 522
List of positive integer factors of 522 that divides 522 without a remainder.
1,2,3,6,9,18,29,58,87,174,261,522
Factors of 354
List of positive integer factors of 354 that divides 354 without a remainder.
1,2,3,6,59,118,177,354
Factors of 728
List of positive integer factors of 728 that divides 728 without a remainder.
1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 522,354,728 . The biggest common factor number is the GCF number.
So the greatest common factor 522,354,728 is 2.
Lets's calculate LCM of 36,51,77
3 | 36, 51, 77 |
12, 17, 77 |
∴ So the LCM of the given numbers is 3 x 12 x 17 x 77 = 47124
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/47124
Therefore, the GCF of Fractions 522/36,354/51,728/77 is 2/47124
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 36,51,77 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,51,77) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(36,51,77) x common factors =1 x 3 = 3
LCM(36,51,77) = ( 36 × 51 × 77 ) / 3
LCM(36,51,77) = 141372 / 3
LCM(36,51,77) = 47124
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 522/36, 354/51, 728/77?
Answer: GCF of Numerators as per given numbers 522/36, 354/51, 728/77 is
GCF of Numerators i.e. for 522,354,728 is 2
LCM of denominators i.e. for 36,51,77 is 47124.
Thus, GCF of Fractions is 2/47124.Finally, GCF of Fractions for 522/36, 354/51, 728/77 is 2/47124.