Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 25/14,68/78,42/11,75/33
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 25,68,42,75
Greatest Common Factor of Numerators i.e. GCF of 25,68,42,75 is 1 .
LCM of Denominators means LCM of 14,78,11,33 as per the given fractions.
LCM of 14,78,11,33 is 6006 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 25,68,42,75
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Greatest Common Factor
We found the factors 25,68,42,75 . The biggest common factor number is the GCF number.
So the greatest common factor 25,68,42,75 is 1.
Lets's calculate LCM of 14,78,11,33
2 | 14, 78, 11, 33 |
3 | 7, 39, 11, 33 |
11 | 7, 13, 11, 11 |
7, 13, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 7 x 13 x 1 x 1 = 6006
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6006
Therefore, the GCF of Fractions 25/14,68/78,42/11,75/33 is 1/6006
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 14,78,11,33 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,78,11,33) = 1
common factors(in case of two or more numbers have common factors) = 66
GCF(14,78,11,33) x common factors =1 x 66 = 66
LCM(14,78,11,33) = ( 14 × 78 × 11 × 33 ) / 66
LCM(14,78,11,33) = 396396 / 66
LCM(14,78,11,33) = 6006
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 25/14, 68/78, 42/11, 75/33?
Answer: GCF of Numerators as per given numbers 25/14, 68/78, 42/11, 75/33 is
GCF of Numerators i.e. for 25,68,42,75 is 1
LCM of denominators i.e. for 14,78,11,33 is 6006.
Thus, GCF of Fractions is 1/6006.Finally, GCF of Fractions for 25/14, 68/78, 42/11, 75/33 is 1/6006.