GCF of 122/87, 305/566
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 122/87, 305/566 i.e 61/49242 easily. The following is the detailed procedure to determine the greatest common factor of fractions 122/87, 305/566.
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 122/87,305/566?
Given fractions are 122/87,305/566
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 122/87,305/566, numerators are 122,305
Denominators are 87,566
The GCF of 122,305 is 61 .
LCM of 87,566 is 49242.
The greatest common factor of 122/87,305/566 = [GCF of 122,305]/[LCM of 87,566]= 61/49242
Therefore, the GCF of 122/87,305/566 is 61/49242.
To find the highest common factor of 122,305, we have to find the factors of both numbers and list the highest common factor.
The factors of 122 are 1, 2, 61, 122
The factors of 305 are 1, 5, 61, 305
The HCF of 122,305 is 61.
Lets's calculate GCF of 122,305
| 61 | 122, 305 |
| 2, 5 |
∴ So the GCF of the given numbers is 61 = 61
Greatest Common Factor of 122,305 By Matching Biggest Common Factor Method
Now, list down the factors of 122
:1,2,61,122
Now, list down the factors of 305
:1,5,61,305
Greatest Common Factor
We found the factors 122,305 . The biggest common factor number is the GCF number.
So the greatest common factor 122,305 is 61.
Lets's calculate LCM of 87,566
Given numbers has no common factors except 1. So, there LCM is their product i.e 49242
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 61/49242
Therefore, the GCF of Fractions 122/87,305/566 is 61/49242
Least Common Multiple of 87,566 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 87,566 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,566) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(87,566) x common factors =1 x 1 = 1
LCM(87,566) = ( 87 × 566 ) / 1
LCM(87,566) = 49242 / 1
LCM(87,566) = 49242
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 122/87, 305/566
1. What is the HCF of 122,305?
The HCF of 122,305 is 61
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 122/87, 305/566?
Answer: GCF of Numerators as per given numbers 122/87, 305/566 is
GCF of Numerators i.e. for 122,305 is 61
LCM of denominators i.e. for 87,566 is 49242.
Thus, GCF of Fractions is 61/49242.Finally, GCF of Fractions for 122/87, 305/566 is 61/49242.