GCF of 412/565, 2678/129
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 412/565, 2678/129 i.e 206/72885 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/565, 2678/129.
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 412/565,2678/129?
Given fractions are 412/565,2678/129
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 412/565,2678/129, numerators are 412,2678
Denominators are 565,129
The GCF of 412,2678 is 206 .
LCM of 565,129 is 72885.
The greatest common factor of 412/565,2678/129 = [GCF of 412,2678]/[LCM of 565,129]= 206/72885
Therefore, the GCF of 412/565,2678/129 is 206/72885.
To find the highest common factor of 412,2678, we have to find the factors of both numbers and list the highest common factor.
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 2678 are 1, 2, 13, 26, 103, 206, 1339, 2678
The HCF of 412,2678 is 206.
Lets's calculate GCF of 412,2678
| 2 | 412, 2678 |
| 103 | 206, 1339 |
| 2, 13 |
∴ So the GCF of the given numbers is 2 x 103 = 206
Greatest Common Factor of 412,2678 By Matching Biggest Common Factor Method
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 2678
:1,2,13,26,103,206,1339,2678
Greatest Common Factor
We found the factors 412,2678 . The biggest common factor number is the GCF number.
So the greatest common factor 412,2678 is 206.
Lets's calculate LCM of 565,129
Given numbers has no common factors except 1. So, there LCM is their product i.e 72885
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 206/72885
Therefore, the GCF of Fractions 412/565,2678/129 is 206/72885
Least Common Multiple of 565,129 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 565,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(565,129) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(565,129) x common factors =1 x 1 = 1
LCM(565,129) = ( 565 × 129 ) / 1
LCM(565,129) = 72885 / 1
LCM(565,129) = 72885
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FAQs on GCF of Fractions of 412/565, 2678/129
1. What is the HCF of 412,2678?
The HCF of 412,2678 is 206
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 412/565, 2678/129?
Answer: GCF of Numerators as per given numbers 412/565, 2678/129 is
GCF of Numerators i.e. for 412,2678 is 206
LCM of denominators i.e. for 565,129 is 72885.
Thus, GCF of Fractions is 206/72885.Finally, GCF of Fractions for 412/565, 2678/129 is 206/72885.