Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 213/67,6123/974
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 213,6123
Greatest Common Factor of Numerators i.e. GCF of 213,6123 is 3 .
LCM of Denominators means LCM of 67,974 as per the given fractions.
LCM of 67,974 is 65258 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 213,6123
3 | 213, 6123 |
71, 2041 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1,3,71,213
Factors of 6123
List of positive integer factors of 6123 that divides 6123 without a remainder.
1,3,13,39,157,471,2041,6123
Greatest Common Factor
We found the factors 213,6123 . The biggest common factor number is the GCF number.
So the greatest common factor 213,6123 is 3.
Lets's calculate LCM of 67,974
Given numbers has no common factors except 1. So, there LCM is their product i.e 65258
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/65258
Therefore, the GCF of Fractions 213/67,6123/974 is 3/65258
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 67,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,974) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,974) x common factors =1 x 1 = 1
LCM(67,974) = ( 67 × 974 ) / 1
LCM(67,974) = 65258 / 1
LCM(67,974) = 65258
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 213/67, 6123/974?
Answer: GCF of Numerators as per given numbers 213/67, 6123/974 is
GCF of Numerators i.e. for 213,6123 is 3
LCM of denominators i.e. for 67,974 is 65258.
Thus, GCF of Fractions is 3/65258.Finally, GCF of Fractions for 213/67, 6123/974 is 3/65258.