GCF of 7682/728, 3909/6912
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7682/728, 3909/6912 i.e 1/628992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7682/728, 3909/6912.
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 7682/728,3909/6912?
Given fractions are 7682/728,3909/6912
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 7682/728,3909/6912, numerators are 7682,3909
Denominators are 728,6912
The GCF of 7682,3909 is 1 .
LCM of 728,6912 is 628992.
The greatest common factor of 7682/728,3909/6912 = [GCF of 7682,3909]/[LCM of 728,6912]= 1/628992
Therefore, the GCF of 7682/728,3909/6912 is 1/628992.
To find the highest common factor of 7682,3909, we have to find the factors of both numbers and list the highest common factor.
The factors of 7682 are 1, 2, 23, 46, 167, 334, 3841, 7682
The factors of 3909 are 1, 3, 1303, 3909
The HCF of 7682,3909 is 1.
Lets's calculate GCF of 7682,3909
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7682,3909 By Matching Biggest Common Factor Method
Now, list down the factors of 7682
:1,2,23,46,167,334,3841,7682
Now, list down the factors of 3909
:1,3,1303,3909
Greatest Common Factor
We found the factors 7682,3909 . The biggest common factor number is the GCF number.
So the greatest common factor 7682,3909 is 1.
Lets's calculate LCM of 728,6912
| 2 | 728, 6912 |
| 2 | 364, 3456 |
| 2 | 182, 1728 |
| 91, 864 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 91 x 864 = 628992
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/628992
Therefore, the GCF of Fractions 7682/728,3909/6912 is 1/628992
Least Common Multiple of 728,6912 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 728,6912 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(728,6912) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(728,6912) x common factors =8 x 1 = 8
LCM(728,6912) = ( 728 × 6912 ) / 8
LCM(728,6912) = 5031936 / 8
LCM(728,6912) = 628992
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FAQs on GCF of Fractions of 7682/728, 3909/6912
1. What is the HCF of 7682,3909?
The HCF of 7682,3909 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 7682/728, 3909/6912?
Answer: GCF of Numerators as per given numbers 7682/728, 3909/6912 is
GCF of Numerators i.e. for 7682,3909 is 1
LCM of denominators i.e. for 728,6912 is 628992.
Thus, GCF of Fractions is 1/628992.Finally, GCF of Fractions for 7682/728, 3909/6912 is 1/628992.