Use our free GCF of Fractions Calculator tool to compute the GCF of 612/202, 136/172 i.e 68/17372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 612/202, 136/172.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 612/202,136/172
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 612/202,136/172, numerators are 612,136
Denominators are 202,172
The GCF of 612,136 is 68 .
LCM of 202,172 is 17372.
The greatest common factor of 612/202,136/172 = [GCF of 612,136]/[LCM of 202,172]= 68/17372
Therefore, the GCF of 612/202,136/172 is 68/17372.
To find the highest common factor of 612,136, we have to find the factors of both numbers and list the highest common factor.
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136
The HCF of 612,136 is 68.
Lets's calculate GCF of 612,136
2 | 612, 136 |
2 | 306, 68 |
17 | 153, 34 |
9, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 17 = 68
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Now, list down the factors of 136
:1,2,4,8,17,34,68,136
Greatest Common Factor
We found the factors 612,136 . The biggest common factor number is the GCF number.
So the greatest common factor 612,136 is 68.
Lets's calculate LCM of 202,172
2 | 202, 172 |
101, 86 |
∴ So the LCM of the given numbers is 2 x 101 x 86 = 17372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 68/17372
Therefore, the GCF of Fractions 612/202,136/172 is 68/17372
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 202,172 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(202,172) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(202,172) x common factors =2 x 1 = 2
LCM(202,172) = ( 202 × 172 ) / 2
LCM(202,172) = 34744 / 2
LCM(202,172) = 17372
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 612,136?
The HCF of 612,136 is 68
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 612/202, 136/172?
Answer: GCF of Numerators as per given numbers 612/202, 136/172 is
GCF of Numerators i.e. for 612,136 is 68
LCM of denominators i.e. for 202,172 is 17372.
Thus, GCF of Fractions is 68/17372.Finally, GCF of Fractions for 612/202, 136/172 is 68/17372.