Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 16/98,78/21,30/59,90/637
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 16,78,30,90
Greatest Common Factor of Numerators i.e. GCF of 16,78,30,90 is 2 .
LCM of Denominators means LCM of 98,21,59,637 as per the given fractions.
LCM of 98,21,59,637 is 225498 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 16,78,30,90
2 | 16, 78, 30, 90 |
8, 39, 15, 45 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Greatest Common Factor
We found the factors 16,78,30,90 . The biggest common factor number is the GCF number.
So the greatest common factor 16,78,30,90 is 2.
Lets's calculate LCM of 98,21,59,637
7 | 98, 21, 59, 637 |
7 | 14, 3, 59, 91 |
2, 3, 59, 13 |
∴ So the LCM of the given numbers is 7 x 7 x 2 x 3 x 59 x 13 = 225498
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/225498
Therefore, the GCF of Fractions 16/98,78/21,30/59,90/637 is 2/225498
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 98,21,59,637 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(98,21,59,637) = 1
common factors(in case of two or more numbers have common factors) = 343
GCF(98,21,59,637) x common factors =1 x 343 = 343
LCM(98,21,59,637) = ( 98 × 21 × 59 × 637 ) / 343
LCM(98,21,59,637) = 77345814 / 343
LCM(98,21,59,637) = 225498
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 16/98, 78/21, 30/59, 90/637?
Answer: GCF of Numerators as per given numbers 16/98, 78/21, 30/59, 90/637 is
GCF of Numerators i.e. for 16,78,30,90 is 2
LCM of denominators i.e. for 98,21,59,637 is 225498.
Thus, GCF of Fractions is 2/225498.Finally, GCF of Fractions for 16/98, 78/21, 30/59, 90/637 is 2/225498.