Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/13,10/63,91/63,273/21
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 68,10,91,273
Greatest Common Factor of Numerators i.e. GCF of 68,10,91,273 is 1 .
LCM of Denominators means LCM of 13,63,63,21 as per the given fractions.
LCM of 13,63,63,21 is 819 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 68,10,91,273
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
Factors of 91
List of positive integer factors of 91 that divides 91 without a remainder.
1,7,13,91
Factors of 273
List of positive integer factors of 273 that divides 273 without a remainder.
1,3,7,13,21,39,91,273
Greatest Common Factor
We found the factors 68,10,91,273 . The biggest common factor number is the GCF number.
So the greatest common factor 68,10,91,273 is 1.
Lets's calculate LCM of 13,63,63,21
3 | 13, 63, 63, 21 |
3 | 13, 21, 21, 7 |
7 | 13, 7, 7, 7 |
13, 1, 1, 1 |
∴ So the LCM of the given numbers is 3 x 3 x 7 x 13 x 1 x 1 x 1 = 819
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/819
Therefore, the GCF of Fractions 68/13,10/63,91/63,273/21 is 1/819
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 13,63,63,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,63,63,21) = 1
common factors(in case of two or more numbers have common factors) = 1323
GCF(13,63,63,21) x common factors =1 x 1323 = 1323
LCM(13,63,63,21) = ( 13 × 63 × 63 × 21 ) / 1323
LCM(13,63,63,21) = 1083537 / 1323
LCM(13,63,63,21) = 819
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 68/13, 10/63, 91/63, 273/21?
Answer: GCF of Numerators as per given numbers 68/13, 10/63, 91/63, 273/21 is
GCF of Numerators i.e. for 68,10,91,273 is 1
LCM of denominators i.e. for 13,63,63,21 is 819.
Thus, GCF of Fractions is 1/819.Finally, GCF of Fractions for 68/13, 10/63, 91/63, 273/21 is 1/819.