GCF of 867/29, 678/261
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 867/29, 678/261 i.e 3/261 easily. The following is the detailed procedure to determine the greatest common factor of fractions 867/29, 678/261.
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 867/29,678/261?
Given fractions are 867/29,678/261
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 867/29,678/261, numerators are 867,678
Denominators are 29,261
The GCF of 867,678 is 3 .
LCM of 29,261 is 261.
The greatest common factor of 867/29,678/261 = [GCF of 867,678]/[LCM of 29,261]= 3/261
Therefore, the GCF of 867/29,678/261 is 3/261.
To find the highest common factor of 867,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 867 are 1, 3, 17, 51, 289, 867
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 867,678 is 3.
Lets's calculate GCF of 867,678
| 3 | 867, 678 |
| 289, 226 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 867,678 By Matching Biggest Common Factor Method
Now, list down the factors of 867
:1,3,17,51,289,867
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 867,678 . The biggest common factor number is the GCF number.
So the greatest common factor 867,678 is 3.
Lets's calculate LCM of 29,261
| 29 | 29, 261 |
| 1, 9 |
∴ So the LCM of the given numbers is 29 x 1 x 9 = 261
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/261
Therefore, the GCF of Fractions 867/29,678/261 is 3/261
Least Common Multiple of 29,261 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 29,261 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,261) = 29
common factors(in case of two or more numbers have common factors) = 1
GCF(29,261) x common factors =29 x 1 = 29
LCM(29,261) = ( 29 × 261 ) / 29
LCM(29,261) = 7569 / 29
LCM(29,261) = 261
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FAQs on GCF of Fractions of 867/29, 678/261
1. What is the HCF of 867,678?
The HCF of 867,678 is 3
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 867/29, 678/261?
Answer: GCF of Numerators as per given numbers 867/29, 678/261 is
GCF of Numerators i.e. for 867,678 is 3
LCM of denominators i.e. for 29,261 is 261.
Thus, GCF of Fractions is 3/261.Finally, GCF of Fractions for 867/29, 678/261 is 3/261.