Use our free GCF of Fractions Calculator tool to compute the GCF of 93/60, 189/84, 102/461 i.e 3/193620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 93/60, 189/84, 102/461.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 93/60,189/84,102/461
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 93/60,189/84,102/461, numerators are 93,189,102
Denominators are 60,84,461
The GCF of 93,189,102 is 3 .
LCM of 60,84,461 is 193620.
The greatest common factor of 93/60,189/84,102/461 = [GCF of 93,189,102]/[LCM of 60,84,461]= 3/193620
Therefore, the GCF of 93/60,189/84,102/461 is 3/193620.
To find the highest common factor of 93,189,102, we have to find the factors of both numbers and list the highest common factor.
The factors of 93 are 1, 3, 31, 93
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The HCF of 93,189,102 is 3.
Lets's calculate GCF of 93,189,102
3 | 93, 189, 102 |
31, 63, 34 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 93
:1,3,31,93
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Greatest Common Factor
We found the factors 93,189,102 . The biggest common factor number is the GCF number.
So the greatest common factor 93,189,102 is 3.
Lets's calculate LCM of 60,84,461
2 | 60, 84, 461 |
2 | 30, 42, 461 |
3 | 15, 21, 461 |
5, 7, 461 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 461 = 193620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/193620
Therefore, the GCF of Fractions 93/60,189/84,102/461 is 3/193620
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 60,84,461 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,84,461) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(60,84,461) x common factors =1 x 12 = 12
LCM(60,84,461) = ( 60 × 84 × 461 ) / 12
LCM(60,84,461) = 2323440 / 12
LCM(60,84,461) = 193620
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 93,189,102?
The HCF of 93,189,102 is 3
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 93/60, 189/84, 102/461?
Answer: GCF of Numerators as per given numbers 93/60, 189/84, 102/461 is
GCF of Numerators i.e. for 93,189,102 is 3
LCM of denominators i.e. for 60,84,461 is 193620.
Thus, GCF of Fractions is 3/193620.Finally, GCF of Fractions for 93/60, 189/84, 102/461 is 3/193620.