Use our free GCF of Fractions Calculator tool to compute the GCF of 243/172, 846/116 i.e 9/4988 easily. The following is the detailed procedure to determine the greatest common factor of fractions 243/172, 846/116.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 243/172,846/116
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 243/172,846/116, numerators are 243,846
Denominators are 172,116
The GCF of 243,846 is 9 .
LCM of 172,116 is 4988.
The greatest common factor of 243/172,846/116 = [GCF of 243,846]/[LCM of 172,116]= 9/4988
Therefore, the GCF of 243/172,846/116 is 9/4988.
To find the highest common factor of 243,846, we have to find the factors of both numbers and list the highest common factor.
The factors of 243 are 1, 3, 9, 27, 81, 243
The factors of 846 are 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846
The HCF of 243,846 is 9.
Lets's calculate GCF of 243,846
3 | 243, 846 |
3 | 81, 282 |
27, 94 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 243
:1,3,9,27,81,243
Now, list down the factors of 846
:1,2,3,6,9,18,47,94,141,282,423,846
Greatest Common Factor
We found the factors 243,846 . The biggest common factor number is the GCF number.
So the greatest common factor 243,846 is 9.
Lets's calculate LCM of 172,116
2 | 172, 116 |
2 | 86, 58 |
43, 29 |
∴ So the LCM of the given numbers is 2 x 2 x 43 x 29 = 4988
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/4988
Therefore, the GCF of Fractions 243/172,846/116 is 9/4988
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 172,116 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,116) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(172,116) x common factors =4 x 1 = 4
LCM(172,116) = ( 172 × 116 ) / 4
LCM(172,116) = 19952 / 4
LCM(172,116) = 4988
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 243,846?
The HCF of 243,846 is 9
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 243/172, 846/116?
Answer: GCF of Numerators as per given numbers 243/172, 846/116 is
GCF of Numerators i.e. for 243,846 is 9
LCM of denominators i.e. for 172,116 is 4988.
Thus, GCF of Fractions is 9/4988.Finally, GCF of Fractions for 243/172, 846/116 is 9/4988.