GCF of 928/404, 1689/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 928/404, 1689/214 i.e 1/43228 easily. The following is the detailed procedure to determine the greatest common factor of fractions 928/404, 1689/214.
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 928/404,1689/214?
Given fractions are 928/404,1689/214
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 928/404,1689/214, numerators are 928,1689
Denominators are 404,214
The GCF of 928,1689 is 1 .
LCM of 404,214 is 43228.
The greatest common factor of 928/404,1689/214 = [GCF of 928,1689]/[LCM of 404,214]= 1/43228
Therefore, the GCF of 928/404,1689/214 is 1/43228.
To find the highest common factor of 928,1689, we have to find the factors of both numbers and list the highest common factor.
The factors of 928 are 1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928
The factors of 1689 are 1, 3, 563, 1689
The HCF of 928,1689 is 1.
Lets's calculate GCF of 928,1689
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 928,1689 By Matching Biggest Common Factor Method
Now, list down the factors of 928
:1,2,4,8,16,29,32,58,116,232,464,928
Now, list down the factors of 1689
:1,3,563,1689
Greatest Common Factor
We found the factors 928,1689 . The biggest common factor number is the GCF number.
So the greatest common factor 928,1689 is 1.
Lets's calculate LCM of 404,214
| 2 | 404, 214 |
| 202, 107 |
∴ So the LCM of the given numbers is 2 x 202 x 107 = 43228
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43228
Therefore, the GCF of Fractions 928/404,1689/214 is 1/43228
Least Common Multiple of 404,214 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 404,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(404,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(404,214) x common factors =2 x 1 = 2
LCM(404,214) = ( 404 × 214 ) / 2
LCM(404,214) = 86456 / 2
LCM(404,214) = 43228
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 928/404, 1689/214
1. What is the HCF of 928,1689?
The HCF of 928,1689 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 928/404, 1689/214?
Answer: GCF of Numerators as per given numbers 928/404, 1689/214 is
GCF of Numerators i.e. for 928,1689 is 1
LCM of denominators i.e. for 404,214 is 43228.
Thus, GCF of Fractions is 1/43228.Finally, GCF of Fractions for 928/404, 1689/214 is 1/43228.