GCF of 992/614, 777/712
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 992/614, 777/712 i.e 1/218584 easily. The following is the detailed procedure to determine the greatest common factor of fractions 992/614, 777/712.
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 992/614,777/712?
Given fractions are 992/614,777/712
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 992/614,777/712, numerators are 992,777
Denominators are 614,712
The GCF of 992,777 is 1 .
LCM of 614,712 is 218584.
The greatest common factor of 992/614,777/712 = [GCF of 992,777]/[LCM of 614,712]= 1/218584
Therefore, the GCF of 992/614,777/712 is 1/218584.
To find the highest common factor of 992,777, we have to find the factors of both numbers and list the highest common factor.
The factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992
The factors of 777 are 1, 3, 7, 21, 37, 111, 259, 777
The HCF of 992,777 is 1.
Lets's calculate GCF of 992,777
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 992,777 By Matching Biggest Common Factor Method
Now, list down the factors of 992
:1,2,4,8,16,31,32,62,124,248,496,992
Now, list down the factors of 777
:1,3,7,21,37,111,259,777
Greatest Common Factor
We found the factors 992,777 . The biggest common factor number is the GCF number.
So the greatest common factor 992,777 is 1.
Lets's calculate LCM of 614,712
| 2 | 614, 712 |
| 307, 356 |
∴ So the LCM of the given numbers is 2 x 307 x 356 = 218584
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/218584
Therefore, the GCF of Fractions 992/614,777/712 is 1/218584
Least Common Multiple of 614,712 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 614,712 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(614,712) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(614,712) x common factors =2 x 1 = 2
LCM(614,712) = ( 614 × 712 ) / 2
LCM(614,712) = 437168 / 2
LCM(614,712) = 218584
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FAQs on GCF of Fractions of 992/614, 777/712
1. What is the HCF of 992,777?
The HCF of 992,777 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 992/614, 777/712?
Answer: GCF of Numerators as per given numbers 992/614, 777/712 is
GCF of Numerators i.e. for 992,777 is 1
LCM of denominators i.e. for 614,712 is 218584.
Thus, GCF of Fractions is 1/218584.Finally, GCF of Fractions for 992/614, 777/712 is 1/218584.