GCF of 1994/214, 5086/7738
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1994/214, 5086/7738 i.e 2/827966 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1994/214, 5086/7738.
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 1994/214,5086/7738?
Given fractions are 1994/214,5086/7738
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 1994/214,5086/7738, numerators are 1994,5086
Denominators are 214,7738
The GCF of 1994,5086 is 2 .
LCM of 214,7738 is 827966.
The greatest common factor of 1994/214,5086/7738 = [GCF of 1994,5086]/[LCM of 214,7738]= 2/827966
Therefore, the GCF of 1994/214,5086/7738 is 2/827966.
To find the highest common factor of 1994,5086, we have to find the factors of both numbers and list the highest common factor.
The factors of 1994 are 1, 2, 997, 1994
The factors of 5086 are 1, 2, 2543, 5086
The HCF of 1994,5086 is 2.
Lets's calculate GCF of 1994,5086
| 2 | 1994, 5086 |
| 997, 2543 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1994,5086 By Matching Biggest Common Factor Method
Now, list down the factors of 1994
:1,2,997,1994
Now, list down the factors of 5086
:1,2,2543,5086
Greatest Common Factor
We found the factors 1994,5086 . The biggest common factor number is the GCF number.
So the greatest common factor 1994,5086 is 2.
Lets's calculate LCM of 214,7738
| 2 | 214, 7738 |
| 107, 3869 |
∴ So the LCM of the given numbers is 2 x 107 x 3869 = 827966
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/827966
Therefore, the GCF of Fractions 1994/214,5086/7738 is 2/827966
Least Common Multiple of 214,7738 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 214,7738 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,7738) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(214,7738) x common factors =2 x 1 = 2
LCM(214,7738) = ( 214 × 7738 ) / 2
LCM(214,7738) = 1655932 / 2
LCM(214,7738) = 827966
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1994/214, 5086/7738
1. What is the HCF of 1994,5086?
The HCF of 1994,5086 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 1994/214, 5086/7738?
Answer: GCF of Numerators as per given numbers 1994/214, 5086/7738 is
GCF of Numerators i.e. for 1994,5086 is 2
LCM of denominators i.e. for 214,7738 is 827966.
Thus, GCF of Fractions is 2/827966.Finally, GCF of Fractions for 1994/214, 5086/7738 is 2/827966.