Use our free GCF of Fractions Calculator tool to compute the GCF of 992/495, 234/678 i.e 2/111870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 992/495, 234/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 992/495,234/678
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 992/495,234/678, numerators are 992,234
Denominators are 495,678
The GCF of 992,234 is 2 .
LCM of 495,678 is 111870.
The greatest common factor of 992/495,234/678 = [GCF of 992,234]/[LCM of 495,678]= 2/111870
Therefore, the GCF of 992/495,234/678 is 2/111870.
To find the highest common factor of 992,234, 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 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The HCF of 992,234 is 2.
Lets's calculate GCF of 992,234
2 | 992, 234 |
496, 117 |
∴ So the GCF of the given numbers is 2 = 2
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 234
:1,2,3,6,9,13,18,26,39,78,117,234
Greatest Common Factor
We found the factors 992,234 . The biggest common factor number is the GCF number.
So the greatest common factor 992,234 is 2.
Lets's calculate LCM of 495,678
3 | 495, 678 |
165, 226 |
∴ So the LCM of the given numbers is 3 x 165 x 226 = 111870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/111870
Therefore, the GCF of Fractions 992/495,234/678 is 2/111870
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 495,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(495,678) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(495,678) x common factors =3 x 1 = 3
LCM(495,678) = ( 495 × 678 ) / 3
LCM(495,678) = 335610 / 3
LCM(495,678) = 111870
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 992,234?
The HCF of 992,234 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 992/495, 234/678?
Answer: GCF of Numerators as per given numbers 992/495, 234/678 is
GCF of Numerators i.e. for 992,234 is 2
LCM of denominators i.e. for 495,678 is 111870.
Thus, GCF of Fractions is 2/111870.Finally, GCF of Fractions for 992/495, 234/678 is 2/111870.