GCF of 537/34, 765/268
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 537/34, 765/268 i.e 3/4556 easily. The following is the detailed procedure to determine the greatest common factor of fractions 537/34, 765/268.
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 537/34,765/268?
Given fractions are 537/34,765/268
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 537/34,765/268, numerators are 537,765
Denominators are 34,268
The GCF of 537,765 is 3 .
LCM of 34,268 is 4556.
The greatest common factor of 537/34,765/268 = [GCF of 537,765]/[LCM of 34,268]= 3/4556
Therefore, the GCF of 537/34,765/268 is 3/4556.
To find the highest common factor of 537,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 537 are 1, 3, 179, 537
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 537,765 is 3.
Lets's calculate GCF of 537,765
| 3 | 537, 765 |
| 179, 255 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 537,765 By Matching Biggest Common Factor Method
Now, list down the factors of 537
:1,3,179,537
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 537,765 . The biggest common factor number is the GCF number.
So the greatest common factor 537,765 is 3.
Lets's calculate LCM of 34,268
| 2 | 34, 268 |
| 17, 134 |
∴ So the LCM of the given numbers is 2 x 17 x 134 = 4556
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/4556
Therefore, the GCF of Fractions 537/34,765/268 is 3/4556
Least Common Multiple of 34,268 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 34,268 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,268) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,268) x common factors =2 x 1 = 2
LCM(34,268) = ( 34 × 268 ) / 2
LCM(34,268) = 9112 / 2
LCM(34,268) = 4556
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FAQs on GCF of Fractions of 537/34, 765/268
1. What is the HCF of 537,765?
The HCF of 537,765 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 537/34, 765/268?
Answer: GCF of Numerators as per given numbers 537/34, 765/268 is
GCF of Numerators i.e. for 537,765 is 3
LCM of denominators i.e. for 34,268 is 4556.
Thus, GCF of Fractions is 3/4556.Finally, GCF of Fractions for 537/34, 765/268 is 3/4556.