Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 122/49,257/72,290/18
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 122,257,290
Greatest Common Factor of Numerators i.e. GCF of 122,257,290 is 1 .
LCM of Denominators means LCM of 49,72,18 as per the given fractions.
LCM of 49,72,18 is 3528 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 122,257,290
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 122
List of positive integer factors of 122 that divides 122 without a remainder.
1,2,61,122
Factors of 257
List of positive integer factors of 257 that divides 257 without a remainder.
1,257
Factors of 290
List of positive integer factors of 290 that divides 290 without a remainder.
1,2,5,10,29,58,145,290
Greatest Common Factor
We found the factors 122,257,290 . The biggest common factor number is the GCF number.
So the greatest common factor 122,257,290 is 1.
Lets's calculate LCM of 49,72,18
2 | 49, 72, 18 |
3 | 49, 36, 9 |
3 | 49, 12, 3 |
49, 4, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 49 x 4 x 1 = 3528
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3528
Therefore, the GCF of Fractions 122/49,257/72,290/18 is 1/3528
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 49,72,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,72,18) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(49,72,18) x common factors =1 x 18 = 18
LCM(49,72,18) = ( 49 × 72 × 18 ) / 18
LCM(49,72,18) = 63504 / 18
LCM(49,72,18) = 3528
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 122/49, 257/72, 290/18?
Answer: GCF of Numerators as per given numbers 122/49, 257/72, 290/18 is
GCF of Numerators i.e. for 122,257,290 is 1
LCM of denominators i.e. for 49,72,18 is 3528.
Thus, GCF of Fractions is 1/3528.Finally, GCF of Fractions for 122/49, 257/72, 290/18 is 1/3528.