Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 76/70,14/63,265/378
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 76,14,265
Greatest Common Factor of Numerators i.e. GCF of 76,14,265 is 1 .
LCM of Denominators means LCM of 70,63,378 as per the given fractions.
LCM of 70,63,378 is 1890 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 76,14,265
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 265
List of positive integer factors of 265 that divides 265 without a remainder.
1,5,53,265
Greatest Common Factor
We found the factors 76,14,265 . The biggest common factor number is the GCF number.
So the greatest common factor 76,14,265 is 1.
Lets's calculate LCM of 70,63,378
2 | 70, 63, 378 |
3 | 35, 63, 189 |
3 | 35, 21, 63 |
7 | 35, 7, 21 |
5, 1, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 7 x 5 x 1 x 3 = 1890
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1890
Therefore, the GCF of Fractions 76/70,14/63,265/378 is 1/1890
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 70,63,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,63,378) = 7
common factors(in case of two or more numbers have common factors) = 126
GCF(70,63,378) x common factors =7 x 126 = 882
LCM(70,63,378) = ( 70 × 63 × 378 ) / 882
LCM(70,63,378) = 1666980 / 882
LCM(70,63,378) = 1890
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 76/70, 14/63, 265/378?
Answer: GCF of Numerators as per given numbers 76/70, 14/63, 265/378 is
GCF of Numerators i.e. for 76,14,265 is 1
LCM of denominators i.e. for 70,63,378 is 1890.
Thus, GCF of Fractions is 1/1890.Finally, GCF of Fractions for 76/70, 14/63, 265/378 is 1/1890.