Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/51,297/12,138/474
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 36,297,138
Greatest Common Factor of Numerators i.e. GCF of 36,297,138 is 3 .
LCM of Denominators means LCM of 51,12,474 as per the given fractions.
LCM of 51,12,474 is 16116 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 36,297,138
3 | 36, 297, 138 |
12, 99, 46 |
∴ So the GCF of the given numbers is 3 = 3
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 297
List of positive integer factors of 297 that divides 297 without a remainder.
1,3,9,11,27,33,99,297
Factors of 138
List of positive integer factors of 138 that divides 138 without a remainder.
1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 36,297,138 . The biggest common factor number is the GCF number.
So the greatest common factor 36,297,138 is 3.
Lets's calculate LCM of 51,12,474
2 | 51, 12, 474 |
3 | 51, 6, 237 |
17, 2, 79 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 2 x 79 = 16116
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/16116
Therefore, the GCF of Fractions 36/51,297/12,138/474 is 3/16116
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 51,12,474 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,12,474) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(51,12,474) x common factors =3 x 6 = 18
LCM(51,12,474) = ( 51 × 12 × 474 ) / 18
LCM(51,12,474) = 290088 / 18
LCM(51,12,474) = 16116
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 36/51, 297/12, 138/474?
Answer: GCF of Numerators as per given numbers 36/51, 297/12, 138/474 is
GCF of Numerators i.e. for 36,297,138 is 3
LCM of denominators i.e. for 51,12,474 is 16116.
Thus, GCF of Fractions is 3/16116.Finally, GCF of Fractions for 36/51, 297/12, 138/474 is 3/16116.