Use our free GCF of Fractions Calculator tool to compute the GCF of 17/76, 749/34, 721/541 i.e 1/698972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/76, 749/34, 721/541.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/76,749/34,721/541
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 17/76,749/34,721/541, numerators are 17,749,721
Denominators are 76,34,541
The GCF of 17,749,721 is 1 .
LCM of 76,34,541 is 698972.
The greatest common factor of 17/76,749/34,721/541 = [GCF of 17,749,721]/[LCM of 76,34,541]= 1/698972
Therefore, the GCF of 17/76,749/34,721/541 is 1/698972.
To find the highest common factor of 17,749,721, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 749 are 1, 7, 107, 749
The factors of 721 are 1, 7, 103, 721
The HCF of 17,749,721 is 1.
Lets's calculate GCF of 17,749,721
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 17
:1,17
Now, list down the factors of 749
:1,7,107,749
Now, list down the factors of 721
:1,7,103,721
Greatest Common Factor
We found the factors 17,749,721 . The biggest common factor number is the GCF number.
So the greatest common factor 17,749,721 is 1.
Lets's calculate LCM of 76,34,541
2 | 76, 34, 541 |
38, 17, 541 |
∴ So the LCM of the given numbers is 2 x 38 x 17 x 541 = 698972
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/698972
Therefore, the GCF of Fractions 17/76,749/34,721/541 is 1/698972
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 76,34,541 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,34,541) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(76,34,541) x common factors =1 x 2 = 2
LCM(76,34,541) = ( 76 × 34 × 541 ) / 2
LCM(76,34,541) = 1397944 / 2
LCM(76,34,541) = 698972
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 17,749,721?
The HCF of 17,749,721 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 17/76, 749/34, 721/541?
Answer: GCF of Numerators as per given numbers 17/76, 749/34, 721/541 is
GCF of Numerators i.e. for 17,749,721 is 1
LCM of denominators i.e. for 76,34,541 is 698972.
Thus, GCF of Fractions is 1/698972.Finally, GCF of Fractions for 17/76, 749/34, 721/541 is 1/698972.