GCF of 7742/988, 5786/992
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7742/988, 5786/992 i.e 2/245024 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7742/988, 5786/992.
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 7742/988,5786/992?
Given fractions are 7742/988,5786/992
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 7742/988,5786/992, numerators are 7742,5786
Denominators are 988,992
The GCF of 7742,5786 is 2 .
LCM of 988,992 is 245024.
The greatest common factor of 7742/988,5786/992 = [GCF of 7742,5786]/[LCM of 988,992]= 2/245024
Therefore, the GCF of 7742/988,5786/992 is 2/245024.
To find the highest common factor of 7742,5786, we have to find the factors of both numbers and list the highest common factor.
The factors of 7742 are 1, 2, 7, 14, 49, 79, 98, 158, 553, 1106, 3871, 7742
The factors of 5786 are 1, 2, 11, 22, 263, 526, 2893, 5786
The HCF of 7742,5786 is 2.
Lets's calculate GCF of 7742,5786
| 2 | 7742, 5786 |
| 3871, 2893 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7742,5786 By Matching Biggest Common Factor Method
Now, list down the factors of 7742
:1,2,7,14,49,79,98,158,553,1106,3871,7742
Now, list down the factors of 5786
:1,2,11,22,263,526,2893,5786
Greatest Common Factor
We found the factors 7742,5786 . The biggest common factor number is the GCF number.
So the greatest common factor 7742,5786 is 2.
Lets's calculate LCM of 988,992
| 2 | 988, 992 |
| 2 | 494, 496 |
| 247, 248 |
∴ So the LCM of the given numbers is 2 x 2 x 247 x 248 = 245024
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/245024
Therefore, the GCF of Fractions 7742/988,5786/992 is 2/245024
Least Common Multiple of 988,992 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 988,992 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(988,992) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(988,992) x common factors =4 x 1 = 4
LCM(988,992) = ( 988 × 992 ) / 4
LCM(988,992) = 980096 / 4
LCM(988,992) = 245024
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FAQs on GCF of Fractions of 7742/988, 5786/992
1. What is the HCF of 7742,5786?
The HCF of 7742,5786 is 2
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 7742/988, 5786/992?
Answer: GCF of Numerators as per given numbers 7742/988, 5786/992 is
GCF of Numerators i.e. for 7742,5786 is 2
LCM of denominators i.e. for 988,992 is 245024.
Thus, GCF of Fractions is 2/245024.Finally, GCF of Fractions for 7742/988, 5786/992 is 2/245024.