Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 126/237,3978/1507
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 126,3978
Greatest Common Factor of Numerators i.e. GCF of 126,3978 is 18 .
LCM of Denominators means LCM of 237,1507 as per the given fractions.
LCM of 237,1507 is 357159 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 126,3978
2 | 126, 3978 |
3 | 63, 1989 |
3 | 21, 663 |
7, 221 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Factors of 126
List of positive integer factors of 126 that divides 126 without a remainder.
1,2,3,6,7,9,14,18,21,42,63,126
Factors of 3978
List of positive integer factors of 3978 that divides 3978 without a remainder.
1,2,3,6,9,13,17,18,26,34,39,51,78,102,117,153,221,234,306,442,663,1326,1989,3978
Greatest Common Factor
We found the factors 126,3978 . The biggest common factor number is the GCF number.
So the greatest common factor 126,3978 is 18.
Lets's calculate LCM of 237,1507
Given numbers has no common factors except 1. So, there LCM is their product i.e 357159
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/357159
Therefore, the GCF of Fractions 126/237,3978/1507 is 18/357159
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 237,1507 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(237,1507) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(237,1507) x common factors =1 x 1 = 1
LCM(237,1507) = ( 237 × 1507 ) / 1
LCM(237,1507) = 357159 / 1
LCM(237,1507) = 357159
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 126/237, 3978/1507?
Answer: GCF of Numerators as per given numbers 126/237, 3978/1507 is
GCF of Numerators i.e. for 126,3978 is 18
LCM of denominators i.e. for 237,1507 is 357159.
Thus, GCF of Fractions is 18/357159.Finally, GCF of Fractions for 126/237, 3978/1507 is 18/357159.