GCF of 2261/76, 2667/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2261/76, 2667/814 i.e 7/30932 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2261/76, 2667/814.
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 2261/76,2667/814?
Given fractions are 2261/76,2667/814
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 2261/76,2667/814, numerators are 2261,2667
Denominators are 76,814
The GCF of 2261,2667 is 7 .
LCM of 76,814 is 30932.
The greatest common factor of 2261/76,2667/814 = [GCF of 2261,2667]/[LCM of 76,814]= 7/30932
Therefore, the GCF of 2261/76,2667/814 is 7/30932.
To find the highest common factor of 2261,2667, we have to find the factors of both numbers and list the highest common factor.
The factors of 2261 are 1, 7, 17, 19, 119, 133, 323, 2261
The factors of 2667 are 1, 3, 7, 21, 127, 381, 889, 2667
The HCF of 2261,2667 is 7.
Lets's calculate GCF of 2261,2667
| 7 | 2261, 2667 |
| 323, 381 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 2261,2667 By Matching Biggest Common Factor Method
Now, list down the factors of 2261
:1,7,17,19,119,133,323,2261
Now, list down the factors of 2667
:1,3,7,21,127,381,889,2667
Greatest Common Factor
We found the factors 2261,2667 . The biggest common factor number is the GCF number.
So the greatest common factor 2261,2667 is 7.
Lets's calculate LCM of 76,814
| 2 | 76, 814 |
| 38, 407 |
∴ So the LCM of the given numbers is 2 x 38 x 407 = 30932
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/30932
Therefore, the GCF of Fractions 2261/76,2667/814 is 7/30932
Least Common Multiple of 76,814 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 76,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,814) x common factors =2 x 1 = 2
LCM(76,814) = ( 76 × 814 ) / 2
LCM(76,814) = 61864 / 2
LCM(76,814) = 30932
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FAQs on GCF of Fractions of 2261/76, 2667/814
1. What is the HCF of 2261,2667?
The HCF of 2261,2667 is 7
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 2261/76, 2667/814?
Answer: GCF of Numerators as per given numbers 2261/76, 2667/814 is
GCF of Numerators i.e. for 2261,2667 is 7
LCM of denominators i.e. for 76,814 is 30932.
Thus, GCF of Fractions is 7/30932.Finally, GCF of Fractions for 2261/76, 2667/814 is 7/30932.