Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 64/4,40/1,82/7,51/7,756/4,32/3,68/8,268/3,16/8,35/8
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 64,40,82,51,756,32,68,268,16,35
Greatest Common Factor of Numerators i.e. GCF of 64,40,82,51,756,32,68,268,16,35 is 1 .
LCM of Denominators means LCM of 4,1,7,7,4,3,8,3,8,8 as per the given fractions.
LCM of 4,1,7,7,4,3,8,3,8,8 is 168 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 64,40,82,51,756,32,68,268,16,35
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1,2,4,8,16,32,64
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Factors of 756
List of positive integer factors of 756 that divides 756 without a remainder.
1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 268
List of positive integer factors of 268 that divides 268 without a remainder.
1,2,4,67,134,268
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1,5,7,35
Greatest Common Factor
We found the factors 64,40,82,51,756,32,68,268,16,35 . The biggest common factor number is the GCF number.
So the greatest common factor 64,40,82,51,756,32,68,268,16,35 is 1.
Lets's calculate LCM of 4,1,7,7,4,3,8,3,8,8
2 | 4, 1, 7, 7, 4, 3, 8, 3, 8, 8 |
2 | 2, 1, 7, 7, 2, 3, 4, 3, 4, 4 |
2 | 1, 1, 7, 7, 1, 3, 2, 3, 2, 2 |
3 | 1, 1, 7, 7, 1, 3, 1, 3, 1, 1 |
7 | 1, 1, 7, 7, 1, 1, 1, 1, 1, 1 |
1, 1, 1, 1, 1, 1, 1, 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 7 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 168
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/168
Therefore, the GCF of Fractions 64/4,40/1,82/7,51/7,756/4,32/3,68/8,268/3,16/8,35/8 is 1/168
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 4,1,7,7,4,3,8,3,8,8 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(4,1,7,7,4,3,8,3,8,8) = 1
common factors(in case of two or more numbers have common factors) = 21504
GCF(4,1,7,7,4,3,8,3,8,8) x common factors =1 x 21504 = 21504
LCM(4,1,7,7,4,3,8,3,8,8) = ( 4 × 1 × 7 × 7 × 4 × 3 × 8 × 3 × 8 × 8 ) / 21504
LCM(4,1,7,7,4,3,8,3,8,8) = 3612672 / 21504
LCM(4,1,7,7,4,3,8,3,8,8) = 168
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 64/4, 40/1, 82/7, 51/7, 756/4, 32/3, 68/8, 268/3, 16/8, 35/8?
Answer: GCF of Numerators as per given numbers 64/4, 40/1, 82/7, 51/7, 756/4, 32/3, 68/8, 268/3, 16/8, 35/8 is
GCF of Numerators i.e. for 64,40,82,51,756,32,68,268,16,35 is 1
LCM of denominators i.e. for 4,1,7,7,4,3,8,3,8,8 is 168.
Thus, GCF of Fractions is 1/168.Finally, GCF of Fractions for 64/4, 40/1, 82/7, 51/7, 756/4, 32/3, 68/8, 268/3, 16/8, 35/8 is 1/168.