GCF of 9214/342, 7149/752
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9214/342, 7149/752 i.e 1/128592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9214/342, 7149/752.
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 9214/342,7149/752?
Given fractions are 9214/342,7149/752
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 9214/342,7149/752, numerators are 9214,7149
Denominators are 342,752
The GCF of 9214,7149 is 1 .
LCM of 342,752 is 128592.
The greatest common factor of 9214/342,7149/752 = [GCF of 9214,7149]/[LCM of 342,752]= 1/128592
Therefore, the GCF of 9214/342,7149/752 is 1/128592.
To find the highest common factor of 9214,7149, we have to find the factors of both numbers and list the highest common factor.
The factors of 9214 are 1, 2, 17, 34, 271, 542, 4607, 9214
The factors of 7149 are 1, 3, 2383, 7149
The HCF of 9214,7149 is 1.
Lets's calculate GCF of 9214,7149
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 9214,7149 By Matching Biggest Common Factor Method
Now, list down the factors of 9214
:1,2,17,34,271,542,4607,9214
Now, list down the factors of 7149
:1,3,2383,7149
Greatest Common Factor
We found the factors 9214,7149 . The biggest common factor number is the GCF number.
So the greatest common factor 9214,7149 is 1.
Lets's calculate LCM of 342,752
| 2 | 342, 752 |
| 171, 376 |
∴ So the LCM of the given numbers is 2 x 171 x 376 = 128592
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/128592
Therefore, the GCF of Fractions 9214/342,7149/752 is 1/128592
Least Common Multiple of 342,752 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 342,752 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,752) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,752) x common factors =2 x 1 = 2
LCM(342,752) = ( 342 × 752 ) / 2
LCM(342,752) = 257184 / 2
LCM(342,752) = 128592
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 9214/342, 7149/752
1. What is the HCF of 9214,7149?
The HCF of 9214,7149 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 9214/342, 7149/752?
Answer: GCF of Numerators as per given numbers 9214/342, 7149/752 is
GCF of Numerators i.e. for 9214,7149 is 1
LCM of denominators i.e. for 342,752 is 128592.
Thus, GCF of Fractions is 1/128592.Finally, GCF of Fractions for 9214/342, 7149/752 is 1/128592.