Use our free GCF of Fractions Calculator tool to compute the GCF of 81/272, 45/233, 698/204 i.e 1/190128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 81/272, 45/233, 698/204.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 81/272,45/233,698/204
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 81/272,45/233,698/204, numerators are 81,45,698
Denominators are 272,233,204
The GCF of 81,45,698 is 1 .
LCM of 272,233,204 is 190128.
The greatest common factor of 81/272,45/233,698/204 = [GCF of 81,45,698]/[LCM of 272,233,204]= 1/190128
Therefore, the GCF of 81/272,45/233,698/204 is 1/190128.
To find the highest common factor of 81,45,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 81 are 1, 3, 9, 27, 81
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 698 are 1, 2, 349, 698
The HCF of 81,45,698 is 1.
Lets's calculate GCF of 81,45,698
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 81
:1,3,9,27,81
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 81,45,698 . The biggest common factor number is the GCF number.
So the greatest common factor 81,45,698 is 1.
Lets's calculate LCM of 272,233,204
2 | 272, 233, 204 |
2 | 136, 233, 102 |
17 | 68, 233, 51 |
4, 233, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 17 x 4 x 233 x 3 = 190128
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/190128
Therefore, the GCF of Fractions 81/272,45/233,698/204 is 1/190128
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 272,233,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(272,233,204) = 1
common factors(in case of two or more numbers have common factors) = 68
GCF(272,233,204) x common factors =1 x 68 = 68
LCM(272,233,204) = ( 272 × 233 × 204 ) / 68
LCM(272,233,204) = 12928704 / 68
LCM(272,233,204) = 190128
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 81,45,698?
The HCF of 81,45,698 is 1
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 81/272, 45/233, 698/204?
Answer: GCF of Numerators as per given numbers 81/272, 45/233, 698/204 is
GCF of Numerators i.e. for 81,45,698 is 1
LCM of denominators i.e. for 272,233,204 is 190128.
Thus, GCF of Fractions is 1/190128.Finally, GCF of Fractions for 81/272, 45/233, 698/204 is 1/190128.