GCF of 338/85, 546/575
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 338/85, 546/575 i.e 26/9775 easily. The following is the detailed procedure to determine the greatest common factor of fractions 338/85, 546/575.
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 338/85,546/575?
Given fractions are 338/85,546/575
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 338/85,546/575, numerators are 338,546
Denominators are 85,575
The GCF of 338,546 is 26 .
LCM of 85,575 is 9775.
The greatest common factor of 338/85,546/575 = [GCF of 338,546]/[LCM of 85,575]= 26/9775
Therefore, the GCF of 338/85,546/575 is 26/9775.
To find the highest common factor of 338,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 338 are 1, 2, 13, 26, 169, 338
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 338,546 is 26.
Lets's calculate GCF of 338,546
| 2 | 338, 546 |
| 13 | 169, 273 |
| 13, 21 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 338,546 By Matching Biggest Common Factor Method
Now, list down the factors of 338
:1,2,13,26,169,338
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 338,546 . The biggest common factor number is the GCF number.
So the greatest common factor 338,546 is 26.
Lets's calculate LCM of 85,575
| 5 | 85, 575 |
| 17, 115 |
∴ So the LCM of the given numbers is 5 x 17 x 115 = 9775
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/9775
Therefore, the GCF of Fractions 338/85,546/575 is 26/9775
Least Common Multiple of 85,575 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 85,575 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,575) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(85,575) x common factors =5 x 1 = 5
LCM(85,575) = ( 85 × 575 ) / 5
LCM(85,575) = 48875 / 5
LCM(85,575) = 9775
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FAQs on GCF of Fractions of 338/85, 546/575
1. What is the HCF of 338,546?
The HCF of 338,546 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 338/85, 546/575?
Answer: GCF of Numerators as per given numbers 338/85, 546/575 is
GCF of Numerators i.e. for 338,546 is 26
LCM of denominators i.e. for 85,575 is 9775.
Thus, GCF of Fractions is 26/9775.Finally, GCF of Fractions for 338/85, 546/575 is 26/9775.