Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 55/14,59/78,95/39,42/213
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 55,59,95,42
Greatest Common Factor of Numerators i.e. GCF of 55,59,95,42 is 1 .
LCM of Denominators means LCM of 14,78,39,213 as per the given fractions.
LCM of 14,78,39,213 is 38766 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 55,59,95,42
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 55
List of positive integer factors of 55 that divides 55 without a remainder.
1,5,11,55
Factors of 59
List of positive integer factors of 59 that divides 59 without a remainder.
1,59
Factors of 95
List of positive integer factors of 95 that divides 95 without a remainder.
1,5,19,95
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 55,59,95,42 . The biggest common factor number is the GCF number.
So the greatest common factor 55,59,95,42 is 1.
Lets's calculate LCM of 14,78,39,213
2 | 14, 78, 39, 213 |
3 | 7, 39, 39, 213 |
13 | 7, 13, 13, 71 |
7, 1, 1, 71 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 7 x 1 x 1 x 71 = 38766
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38766
Therefore, the GCF of Fractions 55/14,59/78,95/39,42/213 is 1/38766
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 14,78,39,213 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,78,39,213) = 1
common factors(in case of two or more numbers have common factors) = 234
GCF(14,78,39,213) x common factors =1 x 234 = 234
LCM(14,78,39,213) = ( 14 × 78 × 39 × 213 ) / 234
LCM(14,78,39,213) = 9071244 / 234
LCM(14,78,39,213) = 38766
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 55/14, 59/78, 95/39, 42/213?
Answer: GCF of Numerators as per given numbers 55/14, 59/78, 95/39, 42/213 is
GCF of Numerators i.e. for 55,59,95,42 is 1
LCM of denominators i.e. for 14,78,39,213 is 38766.
Thus, GCF of Fractions is 1/38766.Finally, GCF of Fractions for 55/14, 59/78, 95/39, 42/213 is 1/38766.