Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 64/2,40/6,92/3,50/9,744/7,81/1,45/4,837/5,74/7,60/6
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 64,40,92,50,744,81,45,837,74,60
Greatest Common Factor of Numerators i.e. GCF of 64,40,92,50,744,81,45,837,74,60 is 1 .
LCM of Denominators means LCM of 2,6,3,9,7,1,4,5,7,6 as per the given fractions.
LCM of 2,6,3,9,7,1,4,5,7,6 is 1260 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 64,40,92,50,744,81,45,837,74,60
∴ 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 92
List of positive integer factors of 92 that divides 92 without a remainder.
1,2,4,23,46,92
Factors of 50
List of positive integer factors of 50 that divides 50 without a remainder.
1,2,5,10,25,50
Factors of 744
List of positive integer factors of 744 that divides 744 without a remainder.
1,2,3,4,6,8,12,24,31,62,93,124,186,248,372,744
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 837
List of positive integer factors of 837 that divides 837 without a remainder.
1,3,9,27,31,93,279,837
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Greatest Common Factor
We found the factors 64,40,92,50,744,81,45,837,74,60 . The biggest common factor number is the GCF number.
So the greatest common factor 64,40,92,50,744,81,45,837,74,60 is 1.
Lets's calculate LCM of 2,6,3,9,7,1,4,5,7,6
2 | 2, 6, 3, 9, 7, 1, 4, 5, 7, 6 |
3 | 1, 3, 3, 9, 7, 1, 2, 5, 7, 3 |
7 | 1, 1, 1, 1, 7, 1, 2, 5, 7, 3 |
1, 1, 1, 1, 1, 1, 2, 5, 1, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1 x 1 x 1 x 1 x 1 x 1 x 2 x 5 x 1 x 3 = 1260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1260
Therefore, the GCF of Fractions 64/2,40/6,92/3,50/9,744/7,81/1,45/4,837/5,74/7,60/6 is 1/1260
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 2,6,3,9,7,1,4,5,7,6 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(2,6,3,9,7,1,4,5,7,6) = 1
common factors(in case of two or more numbers have common factors) = 1512
GCF(2,6,3,9,7,1,4,5,7,6) x common factors =1 x 1512 = 1512
LCM(2,6,3,9,7,1,4,5,7,6) = ( 2 × 6 × 3 × 9 × 7 × 1 × 4 × 5 × 7 × 6 ) / 1512
LCM(2,6,3,9,7,1,4,5,7,6) = 1905120 / 1512
LCM(2,6,3,9,7,1,4,5,7,6) = 1260
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 64/2, 40/6, 92/3, 50/9, 744/7, 81/1, 45/4, 837/5, 74/7, 60/6?
Answer: GCF of Numerators as per given numbers 64/2, 40/6, 92/3, 50/9, 744/7, 81/1, 45/4, 837/5, 74/7, 60/6 is
GCF of Numerators i.e. for 64,40,92,50,744,81,45,837,74,60 is 1
LCM of denominators i.e. for 2,6,3,9,7,1,4,5,7,6 is 1260.
Thus, GCF of Fractions is 1/1260.Finally, GCF of Fractions for 64/2, 40/6, 92/3, 50/9, 744/7, 81/1, 45/4, 837/5, 74/7, 60/6 is 1/1260.