GCF of 546/269, 676/761
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 546/269, 676/761 i.e 26/204709 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/269, 676/761.
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 546/269,676/761?
Given fractions are 546/269,676/761
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 546/269,676/761, numerators are 546,676
Denominators are 269,761
The GCF of 546,676 is 26 .
LCM of 269,761 is 204709.
The greatest common factor of 546/269,676/761 = [GCF of 546,676]/[LCM of 269,761]= 26/204709
Therefore, the GCF of 546/269,676/761 is 26/204709.
To find the highest common factor of 546,676, 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 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676
The HCF of 546,676 is 26.
Lets's calculate GCF of 546,676
| 2 | 546, 676 |
| 13 | 273, 338 |
| 21, 26 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 546,676 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 676
:1,2,4,13,26,52,169,338,676
Greatest Common Factor
We found the factors 546,676 . The biggest common factor number is the GCF number.
So the greatest common factor 546,676 is 26.
Lets's calculate LCM of 269,761
Given numbers has no common factors except 1. So, there LCM is their product i.e 204709
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/204709
Therefore, the GCF of Fractions 546/269,676/761 is 26/204709
Least Common Multiple of 269,761 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 269,761 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,761) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,761) x common factors =1 x 1 = 1
LCM(269,761) = ( 269 × 761 ) / 1
LCM(269,761) = 204709 / 1
LCM(269,761) = 204709
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FAQs on GCF of Fractions of 546/269, 676/761
1. What is the HCF of 546,676?
The HCF of 546,676 is 26
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 546/269, 676/761?
Answer: GCF of Numerators as per given numbers 546/269, 676/761 is
GCF of Numerators i.e. for 546,676 is 26
LCM of denominators i.e. for 269,761 is 204709.
Thus, GCF of Fractions is 26/204709.Finally, GCF of Fractions for 546/269, 676/761 is 26/204709.