Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 684/51,108/202
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 684,108
Greatest Common Factor of Numerators i.e. GCF of 684,108 is 36 .
LCM of Denominators means LCM of 51,202 as per the given fractions.
LCM of 51,202 is 10302 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 684,108
2 | 684, 108 |
2 | 342, 54 |
3 | 171, 27 |
3 | 57, 9 |
19, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Factors of 684
List of positive integer factors of 684 that divides 684 without a remainder.
1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Factors of 108
List of positive integer factors of 108 that divides 108 without a remainder.
1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 684,108 . The biggest common factor number is the GCF number.
So the greatest common factor 684,108 is 36.
Lets's calculate LCM of 51,202
Given numbers has no common factors except 1. So, there LCM is their product i.e 10302
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/10302
Therefore, the GCF of Fractions 684/51,108/202 is 36/10302
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 51,202 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,202) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,202) x common factors =1 x 1 = 1
LCM(51,202) = ( 51 × 202 ) / 1
LCM(51,202) = 10302 / 1
LCM(51,202) = 10302
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 684/51, 108/202?
Answer: GCF of Numerators as per given numbers 684/51, 108/202 is
GCF of Numerators i.e. for 684,108 is 36
LCM of denominators i.e. for 51,202 is 10302.
Thus, GCF of Fractions is 36/10302.Finally, GCF of Fractions for 684/51, 108/202 is 36/10302.