Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 82/91,99/14,65/22,34/84
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 82,99,65,34
Greatest Common Factor of Numerators i.e. GCF of 82,99,65,34 is 1 .
LCM of Denominators means LCM of 91,14,22,84 as per the given fractions.
LCM of 91,14,22,84 is 12012 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 82,99,65,34
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Greatest Common Factor
We found the factors 82,99,65,34 . The biggest common factor number is the GCF number.
So the greatest common factor 82,99,65,34 is 1.
Lets's calculate LCM of 91,14,22,84
2 | 91, 14, 22, 84 |
7 | 91, 7, 11, 42 |
13, 1, 11, 6 |
∴ So the LCM of the given numbers is 2 x 7 x 13 x 1 x 11 x 6 = 12012
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12012
Therefore, the GCF of Fractions 82/91,99/14,65/22,34/84 is 1/12012
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 91,14,22,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(91,14,22,84) = 1
common factors(in case of two or more numbers have common factors) = 196
GCF(91,14,22,84) x common factors =1 x 196 = 196
LCM(91,14,22,84) = ( 91 × 14 × 22 × 84 ) / 196
LCM(91,14,22,84) = 2354352 / 196
LCM(91,14,22,84) = 12012
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 82/91, 99/14, 65/22, 34/84?
Answer: GCF of Numerators as per given numbers 82/91, 99/14, 65/22, 34/84 is
GCF of Numerators i.e. for 82,99,65,34 is 1
LCM of denominators i.e. for 91,14,22,84 is 12012.
Thus, GCF of Fractions is 1/12012.Finally, GCF of Fractions for 82/91, 99/14, 65/22, 34/84 is 1/12012.