GCF of 728/174, 455/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 728/174, 455/686 i.e 91/59682 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/174, 455/686.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 728/174,455/686?
Given fractions are 728/174,455/686
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 728/174,455/686, numerators are 728,455
Denominators are 174,686
The GCF of 728,455 is 91 .
LCM of 174,686 is 59682.
The greatest common factor of 728/174,455/686 = [GCF of 728,455]/[LCM of 174,686]= 91/59682
Therefore, the GCF of 728/174,455/686 is 91/59682.
To find the highest common factor of 728,455, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The factors of 455 are 1, 5, 7, 13, 35, 65, 91, 455
The HCF of 728,455 is 91.
Lets's calculate GCF of 728,455
| 7 | 728, 455 |
| 13 | 104, 65 |
| 8, 5 |
∴ So the GCF of the given numbers is 7 x 13 = 91
Greatest Common Factor of 728,455 By Matching Biggest Common Factor Method
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Now, list down the factors of 455
:1,5,7,13,35,65,91,455
Greatest Common Factor
We found the factors 728,455 . The biggest common factor number is the GCF number.
So the greatest common factor 728,455 is 91.
Lets's calculate LCM of 174,686
| 2 | 174, 686 |
| 87, 343 |
∴ So the LCM of the given numbers is 2 x 87 x 343 = 59682
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 91/59682
Therefore, the GCF of Fractions 728/174,455/686 is 91/59682
Least Common Multiple of 174,686 with GCF Formula
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 174,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,686) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(174,686) x common factors =2 x 1 = 2
LCM(174,686) = ( 174 × 686 ) / 2
LCM(174,686) = 119364 / 2
LCM(174,686) = 59682
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 728/174, 455/686
1. What is the HCF of 728,455?
The HCF of 728,455 is 91
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 728/174, 455/686?
Answer: GCF of Numerators as per given numbers 728/174, 455/686 is
GCF of Numerators i.e. for 728,455 is 91
LCM of denominators i.e. for 174,686 is 59682.
Thus, GCF of Fractions is 91/59682.Finally, GCF of Fractions for 728/174, 455/686 is 91/59682.