Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/7,79/8,98/2,10/2,492/3,79/3,86/1,390/5,91/2,27/6
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 54,79,98,10,492,79,86,390,91,27
Greatest Common Factor of Numerators i.e. GCF of 54,79,98,10,492,79,86,390,91,27 is 1 .
LCM of Denominators means LCM of 7,8,2,2,3,3,1,5,2,6 as per the given fractions.
LCM of 7,8,2,2,3,3,1,5,2,6 is 840 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 54,79,98,10,492,79,86,390,91,27
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Factors of 79
List of positive integer factors of 79 that divides 79 without a remainder.
1,79
Factors of 98
List of positive integer factors of 98 that divides 98 without a remainder.
1,2,7,14,49,98
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
Factors of 492
List of positive integer factors of 492 that divides 492 without a remainder.
1,2,3,4,6,12,41,82,123,164,246,492
Factors of 79
List of positive integer factors of 79 that divides 79 without a remainder.
1,79
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1,2,43,86
Factors of 390
List of positive integer factors of 390 that divides 390 without a remainder.
1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Factors of 91
List of positive integer factors of 91 that divides 91 without a remainder.
1,7,13,91
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Greatest Common Factor
We found the factors 54,79,98,10,492,79,86,390,91,27 . The biggest common factor number is the GCF number.
So the greatest common factor 54,79,98,10,492,79,86,390,91,27 is 1.
Lets's calculate LCM of 7,8,2,2,3,3,1,5,2,6
2 | 7, 8, 2, 2, 3, 3, 1, 5, 2, 6 |
3 | 7, 4, 1, 1, 3, 3, 1, 5, 1, 3 |
7, 4, 1, 1, 1, 1, 1, 5, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 4 x 1 x 1 x 1 x 1 x 1 x 5 x 1 x 1 = 840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/840
Therefore, the GCF of Fractions 54/7,79/8,98/2,10/2,492/3,79/3,86/1,390/5,91/2,27/6 is 1/840
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 7,8,2,2,3,3,1,5,2,6 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(7,8,2,2,3,3,1,5,2,6) = 1
common factors(in case of two or more numbers have common factors) = 144
GCF(7,8,2,2,3,3,1,5,2,6) x common factors =1 x 144 = 144
LCM(7,8,2,2,3,3,1,5,2,6) = ( 7 × 8 × 2 × 2 × 3 × 3 × 1 × 5 × 2 × 6 ) / 144
LCM(7,8,2,2,3,3,1,5,2,6) = 120960 / 144
LCM(7,8,2,2,3,3,1,5,2,6) = 840
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 54/7, 79/8, 98/2, 10/2, 492/3, 79/3, 86/1, 390/5, 91/2, 27/6?
Answer: GCF of Numerators as per given numbers 54/7, 79/8, 98/2, 10/2, 492/3, 79/3, 86/1, 390/5, 91/2, 27/6 is
GCF of Numerators i.e. for 54,79,98,10,492,79,86,390,91,27 is 1
LCM of denominators i.e. for 7,8,2,2,3,3,1,5,2,6 is 840.
Thus, GCF of Fractions is 1/840.Finally, GCF of Fractions for 54/7, 79/8, 98/2, 10/2, 492/3, 79/3, 86/1, 390/5, 91/2, 27/6 is 1/840.