Use our free GCF of Fractions Calculator tool to compute the GCF of 40/85, 684/48, 634/323 i.e 2/77520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/85, 684/48, 634/323.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/85,684/48,634/323
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 40/85,684/48,634/323, numerators are 40,684,634
Denominators are 85,48,323
The GCF of 40,684,634 is 2 .
LCM of 85,48,323 is 77520.
The greatest common factor of 40/85,684/48,634/323 = [GCF of 40,684,634]/[LCM of 85,48,323]= 2/77520
Therefore, the GCF of 40/85,684/48,634/323 is 2/77520.
To find the highest common factor of 40,684,634, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 634 are 1, 2, 317, 634
The HCF of 40,684,634 is 2.
Lets's calculate GCF of 40,684,634
2 | 40, 684, 634 |
20, 342, 317 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 634
:1,2,317,634
Greatest Common Factor
We found the factors 40,684,634 . The biggest common factor number is the GCF number.
So the greatest common factor 40,684,634 is 2.
Lets's calculate LCM of 85,48,323
17 | 85, 48, 323 |
5, 48, 19 |
∴ So the LCM of the given numbers is 17 x 5 x 48 x 19 = 77520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/77520
Therefore, the GCF of Fractions 40/85,684/48,634/323 is 2/77520
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 85,48,323 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,48,323) = 1
common factors(in case of two or more numbers have common factors) = 17
GCF(85,48,323) x common factors =1 x 17 = 17
LCM(85,48,323) = ( 85 × 48 × 323 ) / 17
LCM(85,48,323) = 1317840 / 17
LCM(85,48,323) = 77520
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 40,684,634?
The HCF of 40,684,634 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 40/85, 684/48, 634/323?
Answer: GCF of Numerators as per given numbers 40/85, 684/48, 634/323 is
GCF of Numerators i.e. for 40,684,634 is 2
LCM of denominators i.e. for 85,48,323 is 77520.
Thus, GCF of Fractions is 2/77520.Finally, GCF of Fractions for 40/85, 684/48, 634/323 is 2/77520.