Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 80/14,77/13,87/80,98/69
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 80,77,87,98
Greatest Common Factor of Numerators i.e. GCF of 80,77,87,98 is 1 .
LCM of Denominators means LCM of 14,13,80,69 as per the given fractions.
LCM of 14,13,80,69 is 502320 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 80,77,87,98
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Factors of 77
List of positive integer factors of 77 that divides 77 without a remainder.
1,7,11,77
Factors of 87
List of positive integer factors of 87 that divides 87 without a remainder.
1,3,29,87
Factors of 98
List of positive integer factors of 98 that divides 98 without a remainder.
1,2,7,14,49,98
Greatest Common Factor
We found the factors 80,77,87,98 . The biggest common factor number is the GCF number.
So the greatest common factor 80,77,87,98 is 1.
Lets's calculate LCM of 14,13,80,69
2 | 14, 13, 80, 69 |
7, 13, 40, 69 |
∴ So the LCM of the given numbers is 2 x 7 x 13 x 40 x 69 = 502320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/502320
Therefore, the GCF of Fractions 80/14,77/13,87/80,98/69 is 1/502320
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 14,13,80,69 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,13,80,69) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(14,13,80,69) x common factors =1 x 2 = 2
LCM(14,13,80,69) = ( 14 × 13 × 80 × 69 ) / 2
LCM(14,13,80,69) = 1004640 / 2
LCM(14,13,80,69) = 502320
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 80/14, 77/13, 87/80, 98/69?
Answer: GCF of Numerators as per given numbers 80/14, 77/13, 87/80, 98/69 is
GCF of Numerators i.e. for 80,77,87,98 is 1
LCM of denominators i.e. for 14,13,80,69 is 502320.
Thus, GCF of Fractions is 1/502320.Finally, GCF of Fractions for 80/14, 77/13, 87/80, 98/69 is 1/502320.