GCF of 3678/746, 2291/7306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3678/746, 2291/7306 i.e 1/2725138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3678/746, 2291/7306.
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 3678/746,2291/7306?
Given fractions are 3678/746,2291/7306
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 3678/746,2291/7306, numerators are 3678,2291
Denominators are 746,7306
The GCF of 3678,2291 is 1 .
LCM of 746,7306 is 2725138.
The greatest common factor of 3678/746,2291/7306 = [GCF of 3678,2291]/[LCM of 746,7306]= 1/2725138
Therefore, the GCF of 3678/746,2291/7306 is 1/2725138.
To find the highest common factor of 3678,2291, we have to find the factors of both numbers and list the highest common factor.
The factors of 3678 are 1, 2, 3, 6, 613, 1226, 1839, 3678
The factors of 2291 are 1, 29, 79, 2291
The HCF of 3678,2291 is 1.
Lets's calculate GCF of 3678,2291
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3678,2291 By Matching Biggest Common Factor Method
Now, list down the factors of 3678
:1,2,3,6,613,1226,1839,3678
Now, list down the factors of 2291
:1,29,79,2291
Greatest Common Factor
We found the factors 3678,2291 . The biggest common factor number is the GCF number.
So the greatest common factor 3678,2291 is 1.
Lets's calculate LCM of 746,7306
| 2 | 746, 7306 |
| 373, 3653 |
∴ So the LCM of the given numbers is 2 x 373 x 3653 = 2725138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2725138
Therefore, the GCF of Fractions 3678/746,2291/7306 is 1/2725138
Least Common Multiple of 746,7306 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 746,7306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(746,7306) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(746,7306) x common factors =2 x 1 = 2
LCM(746,7306) = ( 746 × 7306 ) / 2
LCM(746,7306) = 5450276 / 2
LCM(746,7306) = 2725138
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FAQs on GCF of Fractions of 3678/746, 2291/7306
1. What is the HCF of 3678,2291?
The HCF of 3678,2291 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 3678/746, 2291/7306?
Answer: GCF of Numerators as per given numbers 3678/746, 2291/7306 is
GCF of Numerators i.e. for 3678,2291 is 1
LCM of denominators i.e. for 746,7306 is 2725138.
Thus, GCF of Fractions is 1/2725138.Finally, GCF of Fractions for 3678/746, 2291/7306 is 1/2725138.