GCF of 539/588, 5698/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 539/588, 5698/728 i.e 77/15288 easily. The following is the detailed procedure to determine the greatest common factor of fractions 539/588, 5698/728.
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 539/588,5698/728?
Given fractions are 539/588,5698/728
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 539/588,5698/728, numerators are 539,5698
Denominators are 588,728
The GCF of 539,5698 is 77 .
LCM of 588,728 is 15288.
The greatest common factor of 539/588,5698/728 = [GCF of 539,5698]/[LCM of 588,728]= 77/15288
Therefore, the GCF of 539/588,5698/728 is 77/15288.
To find the highest common factor of 539,5698, we have to find the factors of both numbers and list the highest common factor.
The factors of 539 are 1, 7, 11, 49, 77, 539
The factors of 5698 are 1, 2, 7, 11, 14, 22, 37, 74, 77, 154, 259, 407, 518, 814, 2849, 5698
The HCF of 539,5698 is 77.
Lets's calculate GCF of 539,5698
| 7 | 539, 5698 |
| 11 | 77, 814 |
| 7, 74 |
∴ So the GCF of the given numbers is 7 x 11 = 77
Greatest Common Factor of 539,5698 By Matching Biggest Common Factor Method
Now, list down the factors of 539
:1,7,11,49,77,539
Now, list down the factors of 5698
:1,2,7,11,14,22,37,74,77,154,259,407,518,814,2849,5698
Greatest Common Factor
We found the factors 539,5698 . The biggest common factor number is the GCF number.
So the greatest common factor 539,5698 is 77.
Lets's calculate LCM of 588,728
| 2 | 588, 728 |
| 2 | 294, 364 |
| 7 | 147, 182 |
| 21, 26 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 21 x 26 = 15288
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 77/15288
Therefore, the GCF of Fractions 539/588,5698/728 is 77/15288
Least Common Multiple of 588,728 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 588,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(588,728) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(588,728) x common factors =28 x 1 = 28
LCM(588,728) = ( 588 × 728 ) / 28
LCM(588,728) = 428064 / 28
LCM(588,728) = 15288
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FAQs on GCF of Fractions of 539/588, 5698/728
1. What is the HCF of 539,5698?
The HCF of 539,5698 is 77
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 539/588, 5698/728?
Answer: GCF of Numerators as per given numbers 539/588, 5698/728 is
GCF of Numerators i.e. for 539,5698 is 77
LCM of denominators i.e. for 588,728 is 15288.
Thus, GCF of Fractions is 77/15288.Finally, GCF of Fractions for 539/588, 5698/728 is 77/15288.