Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/51,17/48,342/74
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 40,17,342
Greatest Common Factor of Numerators i.e. GCF of 40,17,342 is 1 .
LCM of Denominators means LCM of 51,48,74 as per the given fractions.
LCM of 51,48,74 is 30192 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 40,17,342
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1,17
Factors of 342
List of positive integer factors of 342 that divides 342 without a remainder.
1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 40,17,342 . The biggest common factor number is the GCF number.
So the greatest common factor 40,17,342 is 1.
Lets's calculate LCM of 51,48,74
2 | 51, 48, 74 |
3 | 51, 24, 37 |
17, 8, 37 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 8 x 37 = 30192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30192
Therefore, the GCF of Fractions 40/51,17/48,342/74 is 1/30192
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 51,48,74 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,48,74) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(51,48,74) x common factors =1 x 6 = 6
LCM(51,48,74) = ( 51 × 48 × 74 ) / 6
LCM(51,48,74) = 181152 / 6
LCM(51,48,74) = 30192
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 40/51, 17/48, 342/74?
Answer: GCF of Numerators as per given numbers 40/51, 17/48, 342/74 is
GCF of Numerators i.e. for 40,17,342 is 1
LCM of denominators i.e. for 51,48,74 is 30192.
Thus, GCF of Fractions is 1/30192.Finally, GCF of Fractions for 40/51, 17/48, 342/74 is 1/30192.