Use our free GCF of Fractions Calculator tool to compute the GCF of 721/172, 814/548 i.e 1/23564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 721/172, 814/548.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 721/172,814/548
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 721/172,814/548, numerators are 721,814
Denominators are 172,548
The GCF of 721,814 is 1 .
LCM of 172,548 is 23564.
The greatest common factor of 721/172,814/548 = [GCF of 721,814]/[LCM of 172,548]= 1/23564
Therefore, the GCF of 721/172,814/548 is 1/23564.
To find the highest common factor of 721,814, we have to find the factors of both numbers and list the highest common factor.
The factors of 721 are 1, 7, 103, 721
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The HCF of 721,814 is 1.
Lets's calculate GCF of 721,814
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 721
:1,7,103,721
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Greatest Common Factor
We found the factors 721,814 . The biggest common factor number is the GCF number.
So the greatest common factor 721,814 is 1.
Lets's calculate LCM of 172,548
2 | 172, 548 |
2 | 86, 274 |
43, 137 |
∴ So the LCM of the given numbers is 2 x 2 x 43 x 137 = 23564
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23564
Therefore, the GCF of Fractions 721/172,814/548 is 1/23564
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 172,548 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,548) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(172,548) x common factors =4 x 1 = 4
LCM(172,548) = ( 172 × 548 ) / 4
LCM(172,548) = 94256 / 4
LCM(172,548) = 23564
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 721,814?
The HCF of 721,814 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 721/172, 814/548?
Answer: GCF of Numerators as per given numbers 721/172, 814/548 is
GCF of Numerators i.e. for 721,814 is 1
LCM of denominators i.e. for 172,548 is 23564.
Thus, GCF of Fractions is 1/23564.Finally, GCF of Fractions for 721/172, 814/548 is 1/23564.