GCF of 569/78, 728/789
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 569/78, 728/789 i.e 1/20514 easily. The following is the detailed procedure to determine the greatest common factor of fractions 569/78, 728/789.
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 569/78,728/789?
Given fractions are 569/78,728/789
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 569/78,728/789, numerators are 569,728
Denominators are 78,789
The GCF of 569,728 is 1 .
LCM of 78,789 is 20514.
The greatest common factor of 569/78,728/789 = [GCF of 569,728]/[LCM of 78,789]= 1/20514
Therefore, the GCF of 569/78,728/789 is 1/20514.
To find the highest common factor of 569,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 569 are 1, 569
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 569,728 is 1.
Lets's calculate GCF of 569,728
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 569,728 By Matching Biggest Common Factor Method
Now, list down the factors of 569
:1,569
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 569,728 . The biggest common factor number is the GCF number.
So the greatest common factor 569,728 is 1.
Lets's calculate LCM of 78,789
| 3 | 78, 789 |
| 26, 263 |
∴ So the LCM of the given numbers is 3 x 26 x 263 = 20514
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20514
Therefore, the GCF of Fractions 569/78,728/789 is 1/20514
Least Common Multiple of 78,789 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 78,789 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,789) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(78,789) x common factors =3 x 1 = 3
LCM(78,789) = ( 78 × 789 ) / 3
LCM(78,789) = 61542 / 3
LCM(78,789) = 20514
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FAQs on GCF of Fractions of 569/78, 728/789
1. What is the HCF of 569,728?
The HCF of 569,728 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 569/78, 728/789?
Answer: GCF of Numerators as per given numbers 569/78, 728/789 is
GCF of Numerators i.e. for 569,728 is 1
LCM of denominators i.e. for 78,789 is 20514.
Thus, GCF of Fractions is 1/20514.Finally, GCF of Fractions for 569/78, 728/789 is 1/20514.