Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/14,84/11,90/49,319/84
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 75,84,90,319
Greatest Common Factor of Numerators i.e. GCF of 75,84,90,319 is 1 .
LCM of Denominators means LCM of 14,11,49,84 as per the given fractions.
LCM of 14,11,49,84 is 6468 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 75,84,90,319
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
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
Factors of 319
List of positive integer factors of 319 that divides 319 without a remainder.
1,11,29,319
Greatest Common Factor
We found the factors 75,84,90,319 . The biggest common factor number is the GCF number.
So the greatest common factor 75,84,90,319 is 1.
Lets's calculate LCM of 14,11,49,84
2 | 14, 11, 49, 84 |
7 | 7, 11, 49, 42 |
1, 11, 7, 6 |
∴ So the LCM of the given numbers is 2 x 7 x 1 x 11 x 7 x 6 = 6468
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6468
Therefore, the GCF of Fractions 75/14,84/11,90/49,319/84 is 1/6468
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 14,11,49,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,11,49,84) = 1
common factors(in case of two or more numbers have common factors) = 98
GCF(14,11,49,84) x common factors =1 x 98 = 98
LCM(14,11,49,84) = ( 14 × 11 × 49 × 84 ) / 98
LCM(14,11,49,84) = 633864 / 98
LCM(14,11,49,84) = 6468
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 75/14, 84/11, 90/49, 319/84?
Answer: GCF of Numerators as per given numbers 75/14, 84/11, 90/49, 319/84 is
GCF of Numerators i.e. for 75,84,90,319 is 1
LCM of denominators i.e. for 14,11,49,84 is 6468.
Thus, GCF of Fractions is 1/6468.Finally, GCF of Fractions for 75/14, 84/11, 90/49, 319/84 is 1/6468.