GCF of 8138/364, 7150/7266
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8138/364, 7150/7266 i.e 26/188916 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8138/364, 7150/7266.
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 8138/364,7150/7266?
Given fractions are 8138/364,7150/7266
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 8138/364,7150/7266, numerators are 8138,7150
Denominators are 364,7266
The GCF of 8138,7150 is 26 .
LCM of 364,7266 is 188916.
The greatest common factor of 8138/364,7150/7266 = [GCF of 8138,7150]/[LCM of 364,7266]= 26/188916
Therefore, the GCF of 8138/364,7150/7266 is 26/188916.
To find the highest common factor of 8138,7150, we have to find the factors of both numbers and list the highest common factor.
The factors of 8138 are 1, 2, 13, 26, 313, 626, 4069, 8138
The factors of 7150 are 1, 2, 5, 10, 11, 13, 22, 25, 26, 50, 55, 65, 110, 130, 143, 275, 286, 325, 550, 650, 715, 1430, 3575, 7150
The HCF of 8138,7150 is 26.
Lets's calculate GCF of 8138,7150
| 2 | 8138, 7150 |
| 13 | 4069, 3575 |
| 313, 275 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 8138,7150 By Matching Biggest Common Factor Method
Now, list down the factors of 8138
:1,2,13,26,313,626,4069,8138
Now, list down the factors of 7150
:1,2,5,10,11,13,22,25,26,50,55,65,110,130,143,275,286,325,550,650,715,1430,3575,7150
Greatest Common Factor
We found the factors 8138,7150 . The biggest common factor number is the GCF number.
So the greatest common factor 8138,7150 is 26.
Lets's calculate LCM of 364,7266
| 2 | 364, 7266 |
| 7 | 182, 3633 |
| 26, 519 |
∴ So the LCM of the given numbers is 2 x 7 x 26 x 519 = 188916
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/188916
Therefore, the GCF of Fractions 8138/364,7150/7266 is 26/188916
Least Common Multiple of 364,7266 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 364,7266 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(364,7266) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(364,7266) x common factors =14 x 1 = 14
LCM(364,7266) = ( 364 × 7266 ) / 14
LCM(364,7266) = 2644824 / 14
LCM(364,7266) = 188916
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FAQs on GCF of Fractions of 8138/364, 7150/7266
1. What is the HCF of 8138,7150?
The HCF of 8138,7150 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 8138/364, 7150/7266?
Answer: GCF of Numerators as per given numbers 8138/364, 7150/7266 is
GCF of Numerators i.e. for 8138,7150 is 26
LCM of denominators i.e. for 364,7266 is 188916.
Thus, GCF of Fractions is 26/188916.Finally, GCF of Fractions for 8138/364, 7150/7266 is 26/188916.