Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 421/54,294/30,610/414
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 421,294,610
Greatest Common Factor of Numerators i.e. GCF of 421,294,610 is 1 .
LCM of Denominators means LCM of 54,30,414 as per the given fractions.
LCM of 54,30,414 is 6210 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 421,294,610
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 421
List of positive integer factors of 421 that divides 421 without a remainder.
1,421
Factors of 294
List of positive integer factors of 294 that divides 294 without a remainder.
1,2,3,6,7,14,21,42,49,98,147,294
Factors of 610
List of positive integer factors of 610 that divides 610 without a remainder.
1,2,5,10,61,122,305,610
Greatest Common Factor
We found the factors 421,294,610 . The biggest common factor number is the GCF number.
So the greatest common factor 421,294,610 is 1.
Lets's calculate LCM of 54,30,414
2 | 54, 30, 414 |
3 | 27, 15, 207 |
3 | 9, 5, 69 |
3, 5, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 5 x 23 = 6210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6210
Therefore, the GCF of Fractions 421/54,294/30,610/414 is 1/6210
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 54,30,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,30,414) = 6
common factors(in case of two or more numbers have common factors) = 18
GCF(54,30,414) x common factors =6 x 18 = 108
LCM(54,30,414) = ( 54 × 30 × 414 ) / 108
LCM(54,30,414) = 670680 / 108
LCM(54,30,414) = 6210
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 421/54, 294/30, 610/414?
Answer: GCF of Numerators as per given numbers 421/54, 294/30, 610/414 is
GCF of Numerators i.e. for 421,294,610 is 1
LCM of denominators i.e. for 54,30,414 is 6210.
Thus, GCF of Fractions is 1/6210.Finally, GCF of Fractions for 421/54, 294/30, 610/414 is 1/6210.