Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/49,46/66,74/96
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 65,46,74
Greatest Common Factor of Numerators i.e. GCF of 65,46,74 is 1 .
LCM of Denominators means LCM of 49,66,96 as per the given fractions.
LCM of 49,66,96 is 51744 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 65,46,74
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Greatest Common Factor
We found the factors 65,46,74 . The biggest common factor number is the GCF number.
So the greatest common factor 65,46,74 is 1.
Lets's calculate LCM of 49,66,96
2 | 49, 66, 96 |
3 | 49, 33, 48 |
49, 11, 16 |
∴ So the LCM of the given numbers is 2 x 3 x 49 x 11 x 16 = 51744
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/51744
Therefore, the GCF of Fractions 65/49,46/66,74/96 is 1/51744
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 49,66,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,66,96) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(49,66,96) x common factors =1 x 6 = 6
LCM(49,66,96) = ( 49 × 66 × 96 ) / 6
LCM(49,66,96) = 310464 / 6
LCM(49,66,96) = 51744
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 65/49, 46/66, 74/96?
Answer: GCF of Numerators as per given numbers 65/49, 46/66, 74/96 is
GCF of Numerators i.e. for 65,46,74 is 1
LCM of denominators i.e. for 49,66,96 is 51744.
Thus, GCF of Fractions is 1/51744.Finally, GCF of Fractions for 65/49, 46/66, 74/96 is 1/51744.