GCF of 546/77, 523/778
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 546/77, 523/778 i.e 1/59906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/77, 523/778.
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 546/77,523/778?
Given fractions are 546/77,523/778
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 546/77,523/778, numerators are 546,523
Denominators are 77,778
The GCF of 546,523 is 1 .
LCM of 77,778 is 59906.
The greatest common factor of 546/77,523/778 = [GCF of 546,523]/[LCM of 77,778]= 1/59906
Therefore, the GCF of 546/77,523/778 is 1/59906.
To find the highest common factor of 546,523, we have to find the factors of both numbers and list the highest common factor.
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The factors of 523 are 1, 523
The HCF of 546,523 is 1.
Lets's calculate GCF of 546,523
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 546,523 By Matching Biggest Common Factor Method
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Now, list down the factors of 523
:1,523
Greatest Common Factor
We found the factors 546,523 . The biggest common factor number is the GCF number.
So the greatest common factor 546,523 is 1.
Lets's calculate LCM of 77,778
Given numbers has no common factors except 1. So, there LCM is their product i.e 59906
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/59906
Therefore, the GCF of Fractions 546/77,523/778 is 1/59906
Least Common Multiple of 77,778 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 77,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,778) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,778) x common factors =1 x 1 = 1
LCM(77,778) = ( 77 × 778 ) / 1
LCM(77,778) = 59906 / 1
LCM(77,778) = 59906
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 546/77, 523/778
1. What is the HCF of 546,523?
The HCF of 546,523 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 546/77, 523/778?
Answer: GCF of Numerators as per given numbers 546/77, 523/778 is
GCF of Numerators i.e. for 546,523 is 1
LCM of denominators i.e. for 77,778 is 59906.
Thus, GCF of Fractions is 1/59906.Finally, GCF of Fractions for 546/77, 523/778 is 1/59906.