Use our free GCF of Fractions Calculator tool to compute the GCF of 14/84, 34/21, 839/682 i.e 1/28644 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/84, 34/21, 839/682.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/84,34/21,839/682
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 14/84,34/21,839/682, numerators are 14,34,839
Denominators are 84,21,682
The GCF of 14,34,839 is 1 .
LCM of 84,21,682 is 28644.
The greatest common factor of 14/84,34/21,839/682 = [GCF of 14,34,839]/[LCM of 84,21,682]= 1/28644
Therefore, the GCF of 14/84,34/21,839/682 is 1/28644.
To find the highest common factor of 14,34,839, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 34 are 1, 2, 17, 34
The factors of 839 are 1, 839
The HCF of 14,34,839 is 1.
Lets's calculate GCF of 14,34,839
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 839
:1,839
Greatest Common Factor
We found the factors 14,34,839 . The biggest common factor number is the GCF number.
So the greatest common factor 14,34,839 is 1.
Lets's calculate LCM of 84,21,682
2 | 84, 21, 682 |
3 | 42, 21, 341 |
7 | 14, 7, 341 |
2, 1, 341 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 2 x 1 x 341 = 28644
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28644
Therefore, the GCF of Fractions 14/84,34/21,839/682 is 1/28644
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 84,21,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,21,682) = 1
common factors(in case of two or more numbers have common factors) = 42
GCF(84,21,682) x common factors =1 x 42 = 42
LCM(84,21,682) = ( 84 × 21 × 682 ) / 42
LCM(84,21,682) = 1203048 / 42
LCM(84,21,682) = 28644
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,34,839?
The HCF of 14,34,839 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 14/84, 34/21, 839/682?
Answer: GCF of Numerators as per given numbers 14/84, 34/21, 839/682 is
GCF of Numerators i.e. for 14,34,839 is 1
LCM of denominators i.e. for 84,21,682 is 28644.
Thus, GCF of Fractions is 1/28644.Finally, GCF of Fractions for 14/84, 34/21, 839/682 is 1/28644.