Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/58,69/91,49/46,78/25
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 77,69,49,78
Greatest Common Factor of Numerators i.e. GCF of 77,69,49,78 is 1 .
LCM of Denominators means LCM of 58,91,46,25 as per the given fractions.
LCM of 58,91,46,25 is 3034850 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 77,69,49,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 77
List of positive integer factors of 77 that divides 77 without a remainder.
1,7,11,77
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 77,69,49,78 . The biggest common factor number is the GCF number.
So the greatest common factor 77,69,49,78 is 1.
Lets's calculate LCM of 58,91,46,25
2 | 58, 91, 46, 25 |
29, 91, 23, 25 |
∴ So the LCM of the given numbers is 2 x 29 x 91 x 23 x 25 = 3034850
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3034850
Therefore, the GCF of Fractions 77/58,69/91,49/46,78/25 is 1/3034850
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 58,91,46,25 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,91,46,25) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(58,91,46,25) x common factors =1 x 2 = 2
LCM(58,91,46,25) = ( 58 × 91 × 46 × 25 ) / 2
LCM(58,91,46,25) = 6069700 / 2
LCM(58,91,46,25) = 3034850
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 77/58, 69/91, 49/46, 78/25?
Answer: GCF of Numerators as per given numbers 77/58, 69/91, 49/46, 78/25 is
GCF of Numerators i.e. for 77,69,49,78 is 1
LCM of denominators i.e. for 58,91,46,25 is 3034850.
Thus, GCF of Fractions is 1/3034850.Finally, GCF of Fractions for 77/58, 69/91, 49/46, 78/25 is 1/3034850.