GCF of 8492/849, 9728/7071
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8492/849, 9728/7071 i.e 4/2001093 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8492/849, 9728/7071.
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 8492/849,9728/7071?
Given fractions are 8492/849,9728/7071
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 8492/849,9728/7071, numerators are 8492,9728
Denominators are 849,7071
The GCF of 8492,9728 is 4 .
LCM of 849,7071 is 2001093.
The greatest common factor of 8492/849,9728/7071 = [GCF of 8492,9728]/[LCM of 849,7071]= 4/2001093
Therefore, the GCF of 8492/849,9728/7071 is 4/2001093.
To find the highest common factor of 8492,9728, we have to find the factors of both numbers and list the highest common factor.
The factors of 8492 are 1, 2, 4, 11, 22, 44, 193, 386, 772, 2123, 4246, 8492
The factors of 9728 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728
The HCF of 8492,9728 is 4.
Lets's calculate GCF of 8492,9728
| 2 | 8492, 9728 |
| 2 | 4246, 4864 |
| 2123, 2432 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 8492,9728 By Matching Biggest Common Factor Method
Now, list down the factors of 8492
:1,2,4,11,22,44,193,386,772,2123,4246,8492
Now, list down the factors of 9728
:1,2,4,8,16,19,32,38,64,76,128,152,256,304,512,608,1216,2432,4864,9728
Greatest Common Factor
We found the factors 8492,9728 . The biggest common factor number is the GCF number.
So the greatest common factor 8492,9728 is 4.
Lets's calculate LCM of 849,7071
| 3 | 849, 7071 |
| 283, 2357 |
∴ So the LCM of the given numbers is 3 x 283 x 2357 = 2001093
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/2001093
Therefore, the GCF of Fractions 8492/849,9728/7071 is 4/2001093
Least Common Multiple of 849,7071 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 849,7071 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(849,7071) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(849,7071) x common factors =3 x 1 = 3
LCM(849,7071) = ( 849 × 7071 ) / 3
LCM(849,7071) = 6003279 / 3
LCM(849,7071) = 2001093
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FAQs on GCF of Fractions of 8492/849, 9728/7071
1. What is the HCF of 8492,9728?
The HCF of 8492,9728 is 4
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 8492/849, 9728/7071?
Answer: GCF of Numerators as per given numbers 8492/849, 9728/7071 is
GCF of Numerators i.e. for 8492,9728 is 4
LCM of denominators i.e. for 849,7071 is 2001093.
Thus, GCF of Fractions is 4/2001093.Finally, GCF of Fractions for 8492/849, 9728/7071 is 4/2001093.