Use our free GCF of Fractions Calculator tool to compute the GCF of 58/84, 734/77, 160/315 i.e 2/13860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 58/84, 734/77, 160/315.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 58/84,734/77,160/315
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 58/84,734/77,160/315, numerators are 58,734,160
Denominators are 84,77,315
The GCF of 58,734,160 is 2 .
LCM of 84,77,315 is 13860.
The greatest common factor of 58/84,734/77,160/315 = [GCF of 58,734,160]/[LCM of 84,77,315]= 2/13860
Therefore, the GCF of 58/84,734/77,160/315 is 2/13860.
To find the highest common factor of 58,734,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 58 are 1, 2, 29, 58
The factors of 734 are 1, 2, 367, 734
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 58,734,160 is 2.
Lets's calculate GCF of 58,734,160
2 | 58, 734, 160 |
29, 367, 80 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 58
:1,2,29,58
Now, list down the factors of 734
:1,2,367,734
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 58,734,160 . The biggest common factor number is the GCF number.
So the greatest common factor 58,734,160 is 2.
Lets's calculate LCM of 84,77,315
3 | 84, 77, 315 |
7 | 28, 77, 105 |
4, 11, 15 |
∴ So the LCM of the given numbers is 3 x 7 x 4 x 11 x 15 = 13860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13860
Therefore, the GCF of Fractions 58/84,734/77,160/315 is 2/13860
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 84,77,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,77,315) = 7
common factors(in case of two or more numbers have common factors) = 21
GCF(84,77,315) x common factors =7 x 21 = 147
LCM(84,77,315) = ( 84 × 77 × 315 ) / 147
LCM(84,77,315) = 2037420 / 147
LCM(84,77,315) = 13860
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 58,734,160?
The HCF of 58,734,160 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 58/84, 734/77, 160/315?
Answer: GCF of Numerators as per given numbers 58/84, 734/77, 160/315 is
GCF of Numerators i.e. for 58,734,160 is 2
LCM of denominators i.e. for 84,77,315 is 13860.
Thus, GCF of Fractions is 2/13860.Finally, GCF of Fractions for 58/84, 734/77, 160/315 is 2/13860.