GCF of 7746/586, 8421/708
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7746/586, 8421/708 i.e 3/207444 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7746/586, 8421/708.
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 7746/586,8421/708?
Given fractions are 7746/586,8421/708
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 7746/586,8421/708, numerators are 7746,8421
Denominators are 586,708
The GCF of 7746,8421 is 3 .
LCM of 586,708 is 207444.
The greatest common factor of 7746/586,8421/708 = [GCF of 7746,8421]/[LCM of 586,708]= 3/207444
Therefore, the GCF of 7746/586,8421/708 is 3/207444.
To find the highest common factor of 7746,8421, we have to find the factors of both numbers and list the highest common factor.
The factors of 7746 are 1, 2, 3, 6, 1291, 2582, 3873, 7746
The factors of 8421 are 1, 3, 7, 21, 401, 1203, 2807, 8421
The HCF of 7746,8421 is 3.
Lets's calculate GCF of 7746,8421
| 3 | 7746, 8421 |
| 2582, 2807 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7746,8421 By Matching Biggest Common Factor Method
Now, list down the factors of 7746
:1,2,3,6,1291,2582,3873,7746
Now, list down the factors of 8421
:1,3,7,21,401,1203,2807,8421
Greatest Common Factor
We found the factors 7746,8421 . The biggest common factor number is the GCF number.
So the greatest common factor 7746,8421 is 3.
Lets's calculate LCM of 586,708
| 2 | 586, 708 |
| 293, 354 |
∴ So the LCM of the given numbers is 2 x 293 x 354 = 207444
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/207444
Therefore, the GCF of Fractions 7746/586,8421/708 is 3/207444
Least Common Multiple of 586,708 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 586,708 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(586,708) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(586,708) x common factors =2 x 1 = 2
LCM(586,708) = ( 586 × 708 ) / 2
LCM(586,708) = 414888 / 2
LCM(586,708) = 207444
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FAQs on GCF of Fractions of 7746/586, 8421/708
1. What is the HCF of 7746,8421?
The HCF of 7746,8421 is 3
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 7746/586, 8421/708?
Answer: GCF of Numerators as per given numbers 7746/586, 8421/708 is
GCF of Numerators i.e. for 7746,8421 is 3
LCM of denominators i.e. for 586,708 is 207444.
Thus, GCF of Fractions is 3/207444.Finally, GCF of Fractions for 7746/586, 8421/708 is 3/207444.