GCF of 868/218, 8414/382
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 868/218, 8414/382 i.e 14/41638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 868/218, 8414/382.
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 868/218,8414/382?
Given fractions are 868/218,8414/382
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 868/218,8414/382, numerators are 868,8414
Denominators are 218,382
The GCF of 868,8414 is 14 .
LCM of 218,382 is 41638.
The greatest common factor of 868/218,8414/382 = [GCF of 868,8414]/[LCM of 218,382]= 14/41638
Therefore, the GCF of 868/218,8414/382 is 14/41638.
To find the highest common factor of 868,8414, we have to find the factors of both numbers and list the highest common factor.
The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868
The factors of 8414 are 1, 2, 7, 14, 601, 1202, 4207, 8414
The HCF of 868,8414 is 14.
Lets's calculate GCF of 868,8414
| 2 | 868, 8414 |
| 7 | 434, 4207 |
| 62, 601 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 868,8414 By Matching Biggest Common Factor Method
Now, list down the factors of 868
:1,2,4,7,14,28,31,62,124,217,434,868
Now, list down the factors of 8414
:1,2,7,14,601,1202,4207,8414
Greatest Common Factor
We found the factors 868,8414 . The biggest common factor number is the GCF number.
So the greatest common factor 868,8414 is 14.
Lets's calculate LCM of 218,382
| 2 | 218, 382 |
| 109, 191 |
∴ So the LCM of the given numbers is 2 x 109 x 191 = 41638
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/41638
Therefore, the GCF of Fractions 868/218,8414/382 is 14/41638
Least Common Multiple of 218,382 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 218,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,382) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,382) x common factors =2 x 1 = 2
LCM(218,382) = ( 218 × 382 ) / 2
LCM(218,382) = 83276 / 2
LCM(218,382) = 41638
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 868/218, 8414/382
1. What is the HCF of 868,8414?
The HCF of 868,8414 is 14
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 868/218, 8414/382?
Answer: GCF of Numerators as per given numbers 868/218, 8414/382 is
GCF of Numerators i.e. for 868,8414 is 14
LCM of denominators i.e. for 218,382 is 41638.
Thus, GCF of Fractions is 14/41638.Finally, GCF of Fractions for 868/218, 8414/382 is 14/41638.