Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 31/9,54/9,88/8,81/1,989/1,22/3,82/2,572/1,36/9,53/2
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 31,54,88,81,989,22,82,572,36,53
Greatest Common Factor of Numerators i.e. GCF of 31,54,88,81,989,22,82,572,36,53 is 1 .
LCM of Denominators means LCM of 9,9,8,1,1,3,2,1,9,2 as per the given fractions.
LCM of 9,9,8,1,1,3,2,1,9,2 is 72 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 31,54,88,81,989,22,82,572,36,53
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
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 88
List of positive integer factors of 88 that divides 88 without a remainder.
1,2,4,8,11,22,44,88
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 989
List of positive integer factors of 989 that divides 989 without a remainder.
1,23,43,989
Factors of 22
List of positive integer factors of 22 that divides 22 without a remainder.
1,2,11,22
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 572
List of positive integer factors of 572 that divides 572 without a remainder.
1,2,4,11,13,22,26,44,52,143,286,572
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 53
List of positive integer factors of 53 that divides 53 without a remainder.
1,53
Greatest Common Factor
We found the factors 31,54,88,81,989,22,82,572,36,53 . The biggest common factor number is the GCF number.
So the greatest common factor 31,54,88,81,989,22,82,572,36,53 is 1.
Lets's calculate LCM of 9,9,8,1,1,3,2,1,9,2
2 | 9, 9, 8, 1, 1, 3, 2, 1, 9, 2 |
3 | 9, 9, 4, 1, 1, 3, 1, 1, 9, 1 |
3 | 1, 3, 4, 1, 1, 3, 1, 1, 3, 1 |
1, 1, 4, 1, 1, 1, 1, 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 1 x 1 x 4 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 72
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72
Therefore, the GCF of Fractions 31/9,54/9,88/8,81/1,989/1,22/3,82/2,572/1,36/9,53/2 is 1/72
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 9,9,8,1,1,3,2,1,9,2 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(9,9,8,1,1,3,2,1,9,2) = 1
common factors(in case of two or more numbers have common factors) = 972
GCF(9,9,8,1,1,3,2,1,9,2) x common factors =1 x 972 = 972
LCM(9,9,8,1,1,3,2,1,9,2) = ( 9 × 9 × 8 × 1 × 1 × 3 × 2 × 1 × 9 × 2 ) / 972
LCM(9,9,8,1,1,3,2,1,9,2) = 69984 / 972
LCM(9,9,8,1,1,3,2,1,9,2) = 72
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 31/9, 54/9, 88/8, 81/1, 989/1, 22/3, 82/2, 572/1, 36/9, 53/2?
Answer: GCF of Numerators as per given numbers 31/9, 54/9, 88/8, 81/1, 989/1, 22/3, 82/2, 572/1, 36/9, 53/2 is
GCF of Numerators i.e. for 31,54,88,81,989,22,82,572,36,53 is 1
LCM of denominators i.e. for 9,9,8,1,1,3,2,1,9,2 is 72.
Thus, GCF of Fractions is 1/72.Finally, GCF of Fractions for 31/9, 54/9, 88/8, 81/1, 989/1, 22/3, 82/2, 572/1, 36/9, 53/2 is 1/72.