Use our free GCF of Fractions Calculator tool to compute the GCF of 1678/960, 1978/3942 i.e 2/630720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1678/960, 1978/3942.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1678/960,1978/3942
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 1678/960,1978/3942, numerators are 1678,1978
Denominators are 960,3942
The GCF of 1678,1978 is 2 .
LCM of 960,3942 is 630720.
The greatest common factor of 1678/960,1978/3942 = [GCF of 1678,1978]/[LCM of 960,3942]= 2/630720
Therefore, the GCF of 1678/960,1978/3942 is 2/630720.
To find the highest common factor of 1678,1978, we have to find the factors of both numbers and list the highest common factor.
The factors of 1678 are 1, 2, 839, 1678
The factors of 1978 are 1, 2, 23, 43, 46, 86, 989, 1978
The HCF of 1678,1978 is 2.
Lets's calculate GCF of 1678,1978
2 | 1678, 1978 |
839, 989 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 1678
:1,2,839,1678
Now, list down the factors of 1978
:1,2,23,43,46,86,989,1978
Greatest Common Factor
We found the factors 1678,1978 . The biggest common factor number is the GCF number.
So the greatest common factor 1678,1978 is 2.
Lets's calculate LCM of 960,3942
2 | 960, 3942 |
3 | 480, 1971 |
160, 657 |
∴ So the LCM of the given numbers is 2 x 3 x 160 x 657 = 630720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/630720
Therefore, the GCF of Fractions 1678/960,1978/3942 is 2/630720
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 960,3942 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(960,3942) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(960,3942) x common factors =6 x 1 = 6
LCM(960,3942) = ( 960 × 3942 ) / 6
LCM(960,3942) = 3784320 / 6
LCM(960,3942) = 630720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 1678,1978?
The HCF of 1678,1978 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 1678/960, 1978/3942?
Answer: GCF of Numerators as per given numbers 1678/960, 1978/3942 is
GCF of Numerators i.e. for 1678,1978 is 2
LCM of denominators i.e. for 960,3942 is 630720.
Thus, GCF of Fractions is 2/630720.Finally, GCF of Fractions for 1678/960, 1978/3942 is 2/630720.