Use our free GCF of Fractions Calculator tool to compute the GCF of 64/71, 116/99, 564/414 i.e 4/323334 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/71, 116/99, 564/414.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 64/71,116/99,564/414
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 64/71,116/99,564/414, numerators are 64,116,564
Denominators are 71,99,414
The GCF of 64,116,564 is 4 .
LCM of 71,99,414 is 323334.
The greatest common factor of 64/71,116/99,564/414 = [GCF of 64,116,564]/[LCM of 71,99,414]= 4/323334
Therefore, the GCF of 64/71,116/99,564/414 is 4/323334.
To find the highest common factor of 64,116,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 116 are 1, 2, 4, 29, 58, 116
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 64,116,564 is 4.
Lets's calculate GCF of 64,116,564
2 | 64, 116, 564 |
2 | 32, 58, 282 |
16, 29, 141 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 116
:1,2,4,29,58,116
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 64,116,564 . The biggest common factor number is the GCF number.
So the greatest common factor 64,116,564 is 4.
Lets's calculate LCM of 71,99,414
3 | 71, 99, 414 |
3 | 71, 33, 138 |
71, 11, 46 |
∴ So the LCM of the given numbers is 3 x 3 x 71 x 11 x 46 = 323334
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/323334
Therefore, the GCF of Fractions 64/71,116/99,564/414 is 4/323334
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 71,99,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,99,414) = 1
common factors(in case of two or more numbers have common factors) = 9
GCF(71,99,414) x common factors =1 x 9 = 9
LCM(71,99,414) = ( 71 × 99 × 414 ) / 9
LCM(71,99,414) = 2910006 / 9
LCM(71,99,414) = 323334
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 64,116,564?
The HCF of 64,116,564 is 4
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 64/71, 116/99, 564/414?
Answer: GCF of Numerators as per given numbers 64/71, 116/99, 564/414 is
GCF of Numerators i.e. for 64,116,564 is 4
LCM of denominators i.e. for 71,99,414 is 323334.
Thus, GCF of Fractions is 4/323334.Finally, GCF of Fractions for 64/71, 116/99, 564/414 is 4/323334.