Use our free GCF of Fractions Calculator tool to compute the GCF of 66/27, 78/692, 546/142 i.e 6/1326564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/27, 78/692, 546/142.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/27,78/692,546/142
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 66/27,78/692,546/142, numerators are 66,78,546
Denominators are 27,692,142
The GCF of 66,78,546 is 6 .
LCM of 27,692,142 is 1326564.
The greatest common factor of 66/27,78/692,546/142 = [GCF of 66,78,546]/[LCM of 27,692,142]= 6/1326564
Therefore, the GCF of 66/27,78/692,546/142 is 6/1326564.
To find the highest common factor of 66,78,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 66,78,546 is 6.
Lets's calculate GCF of 66,78,546
2 | 66, 78, 546 |
3 | 33, 39, 273 |
11, 13, 91 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 66,78,546 . The biggest common factor number is the GCF number.
So the greatest common factor 66,78,546 is 6.
Lets's calculate LCM of 27,692,142
2 | 27, 692, 142 |
27, 346, 71 |
∴ So the LCM of the given numbers is 2 x 27 x 346 x 71 = 1326564
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1326564
Therefore, the GCF of Fractions 66/27,78/692,546/142 is 6/1326564
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 27,692,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,692,142) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(27,692,142) x common factors =1 x 2 = 2
LCM(27,692,142) = ( 27 × 692 × 142 ) / 2
LCM(27,692,142) = 2653128 / 2
LCM(27,692,142) = 1326564
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 66,78,546?
The HCF of 66,78,546 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 66/27, 78/692, 546/142?
Answer: GCF of Numerators as per given numbers 66/27, 78/692, 546/142 is
GCF of Numerators i.e. for 66,78,546 is 6
LCM of denominators i.e. for 27,692,142 is 1326564.
Thus, GCF of Fractions is 6/1326564.Finally, GCF of Fractions for 66/27, 78/692, 546/142 is 6/1326564.