Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 72/76,61/84,390/378
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 72,61,390
Greatest Common Factor of Numerators i.e. GCF of 72,61,390 is 1 .
LCM of Denominators means LCM of 76,84,378 as per the given fractions.
LCM of 76,84,378 is 14364 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 72,61,390
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 390
List of positive integer factors of 390 that divides 390 without a remainder.
1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Greatest Common Factor
We found the factors 72,61,390 . The biggest common factor number is the GCF number.
So the greatest common factor 72,61,390 is 1.
Lets's calculate LCM of 76,84,378
2 | 76, 84, 378 |
2 | 38, 42, 189 |
3 | 19, 21, 189 |
7 | 19, 7, 63 |
19, 1, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 19 x 1 x 9 = 14364
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14364
Therefore, the GCF of Fractions 72/76,61/84,390/378 is 1/14364
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 76,84,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,84,378) = 2
common factors(in case of two or more numbers have common factors) = 84
GCF(76,84,378) x common factors =2 x 84 = 168
LCM(76,84,378) = ( 76 × 84 × 378 ) / 168
LCM(76,84,378) = 2413152 / 168
LCM(76,84,378) = 14364
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 72/76, 61/84, 390/378?
Answer: GCF of Numerators as per given numbers 72/76, 61/84, 390/378 is
GCF of Numerators i.e. for 72,61,390 is 1
LCM of denominators i.e. for 76,84,378 is 14364.
Thus, GCF of Fractions is 1/14364.Finally, GCF of Fractions for 72/76, 61/84, 390/378 is 1/14364.