GCF of 415/65, 546/775
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 415/65, 546/775 i.e 1/10075 easily. The following is the detailed procedure to determine the greatest common factor of fractions 415/65, 546/775.
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 415/65,546/775?
Given fractions are 415/65,546/775
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 415/65,546/775, numerators are 415,546
Denominators are 65,775
The GCF of 415,546 is 1 .
LCM of 65,775 is 10075.
The greatest common factor of 415/65,546/775 = [GCF of 415,546]/[LCM of 65,775]= 1/10075
Therefore, the GCF of 415/65,546/775 is 1/10075.
To find the highest common factor of 415,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 415 are 1, 5, 83, 415
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 415,546 is 1.
Lets's calculate GCF of 415,546
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 415,546 By Matching Biggest Common Factor Method
Now, list down the factors of 415
:1,5,83,415
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 415,546 . The biggest common factor number is the GCF number.
So the greatest common factor 415,546 is 1.
Lets's calculate LCM of 65,775
| 5 | 65, 775 |
| 13, 155 |
∴ So the LCM of the given numbers is 5 x 13 x 155 = 10075
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10075
Therefore, the GCF of Fractions 415/65,546/775 is 1/10075
Least Common Multiple of 65,775 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 65,775 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,775) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(65,775) x common factors =5 x 1 = 5
LCM(65,775) = ( 65 × 775 ) / 5
LCM(65,775) = 50375 / 5
LCM(65,775) = 10075
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FAQs on GCF of Fractions of 415/65, 546/775
1. What is the HCF of 415,546?
The HCF of 415,546 is 1
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 415/65, 546/775?
Answer: GCF of Numerators as per given numbers 415/65, 546/775 is
GCF of Numerators i.e. for 415,546 is 1
LCM of denominators i.e. for 65,775 is 10075.
Thus, GCF of Fractions is 1/10075.Finally, GCF of Fractions for 415/65, 546/775 is 1/10075.