Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8/67,80/49,14/399,400/176
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 8,80,14,400
Greatest Common Factor of Numerators i.e. GCF of 8,80,14,400 is 2 .
LCM of Denominators means LCM of 67,49,399,176 as per the given fractions.
LCM of 67,49,399,176 is 32935056 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 8,80,14,400
2 | 8, 80, 14, 400 |
4, 40, 7, 200 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1,2,4,8
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 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 400
List of positive integer factors of 400 that divides 400 without a remainder.
1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 8,80,14,400 . The biggest common factor number is the GCF number.
So the greatest common factor 8,80,14,400 is 2.
Lets's calculate LCM of 67,49,399,176
7 | 67, 49, 399, 176 |
67, 7, 57, 176 |
∴ So the LCM of the given numbers is 7 x 67 x 7 x 57 x 176 = 32935056
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/32935056
Therefore, the GCF of Fractions 8/67,80/49,14/399,400/176 is 2/32935056
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 67,49,399,176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,49,399,176) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(67,49,399,176) x common factors =1 x 7 = 7
LCM(67,49,399,176) = ( 67 × 49 × 399 × 176 ) / 7
LCM(67,49,399,176) = 230545392 / 7
LCM(67,49,399,176) = 32935056
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 8/67, 80/49, 14/399, 400/176?
Answer: GCF of Numerators as per given numbers 8/67, 80/49, 14/399, 400/176 is
GCF of Numerators i.e. for 8,80,14,400 is 2
LCM of denominators i.e. for 67,49,399,176 is 32935056.
Thus, GCF of Fractions is 2/32935056.Finally, GCF of Fractions for 8/67, 80/49, 14/399, 400/176 is 2/32935056.