Use our free GCF of Fractions Calculator tool to compute the GCF of 36/668, 84/319, 438/517 i.e 6/10015324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 36/668, 84/319, 438/517.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/668,84/319,438/517
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 36/668,84/319,438/517, numerators are 36,84,438
Denominators are 668,319,517
The GCF of 36,84,438 is 6 .
LCM of 668,319,517 is 10015324.
The greatest common factor of 36/668,84/319,438/517 = [GCF of 36,84,438]/[LCM of 668,319,517]= 6/10015324
Therefore, the GCF of 36/668,84/319,438/517 is 6/10015324.
To find the highest common factor of 36,84,438, we have to find the factors of both numbers and list the highest common factor.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The HCF of 36,84,438 is 6.
Lets's calculate GCF of 36,84,438
2 | 36, 84, 438 |
3 | 18, 42, 219 |
6, 14, 73 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Greatest Common Factor
We found the factors 36,84,438 . The biggest common factor number is the GCF number.
So the greatest common factor 36,84,438 is 6.
Lets's calculate LCM of 668,319,517
11 | 668, 319, 517 |
668, 29, 47 |
∴ So the LCM of the given numbers is 11 x 668 x 29 x 47 = 10015324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/10015324
Therefore, the GCF of Fractions 36/668,84/319,438/517 is 6/10015324
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 668,319,517 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(668,319,517) = 1
common factors(in case of two or more numbers have common factors) = 11
GCF(668,319,517) x common factors =1 x 11 = 11
LCM(668,319,517) = ( 668 × 319 × 517 ) / 11
LCM(668,319,517) = 110168564 / 11
LCM(668,319,517) = 10015324
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 36,84,438?
The HCF of 36,84,438 is 6
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 36/668, 84/319, 438/517?
Answer: GCF of Numerators as per given numbers 36/668, 84/319, 438/517 is
GCF of Numerators i.e. for 36,84,438 is 6
LCM of denominators i.e. for 668,319,517 is 10015324.
Thus, GCF of Fractions is 6/10015324.Finally, GCF of Fractions for 36/668, 84/319, 438/517 is 6/10015324.