Use our free GCF of Fractions Calculator tool to compute the GCF of 172/102, 638/472 i.e 2/24072 easily. The following is the detailed procedure to determine the greatest common factor of fractions 172/102, 638/472.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 172/102,638/472
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 172/102,638/472, numerators are 172,638
Denominators are 102,472
The GCF of 172,638 is 2 .
LCM of 102,472 is 24072.
The greatest common factor of 172/102,638/472 = [GCF of 172,638]/[LCM of 102,472]= 2/24072
Therefore, the GCF of 172/102,638/472 is 2/24072.
To find the highest common factor of 172,638, we have to find the factors of both numbers and list the highest common factor.
The factors of 172 are 1, 2, 4, 43, 86, 172
The factors of 638 are 1, 2, 11, 22, 29, 58, 319, 638
The HCF of 172,638 is 2.
Lets's calculate GCF of 172,638
2 | 172, 638 |
86, 319 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 172
:1,2,4,43,86,172
Now, list down the factors of 638
:1,2,11,22,29,58,319,638
Greatest Common Factor
We found the factors 172,638 . The biggest common factor number is the GCF number.
So the greatest common factor 172,638 is 2.
Lets's calculate LCM of 102,472
2 | 102, 472 |
51, 236 |
∴ So the LCM of the given numbers is 2 x 51 x 236 = 24072
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/24072
Therefore, the GCF of Fractions 172/102,638/472 is 2/24072
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 102,472 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,472) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(102,472) x common factors =2 x 1 = 2
LCM(102,472) = ( 102 × 472 ) / 2
LCM(102,472) = 48144 / 2
LCM(102,472) = 24072
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 172,638?
The HCF of 172,638 is 2
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 172/102, 638/472?
Answer: GCF of Numerators as per given numbers 172/102, 638/472 is
GCF of Numerators i.e. for 172,638 is 2
LCM of denominators i.e. for 102,472 is 24072.
Thus, GCF of Fractions is 2/24072.Finally, GCF of Fractions for 172/102, 638/472 is 2/24072.