GCF of 68/75, 70/728, 106/108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 68/75, 70/728, 106/108 i.e 2/491400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/75, 70/728, 106/108.
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 68/75,70/728,106/108?
Given fractions are 68/75,70/728,106/108
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 68/75,70/728,106/108, numerators are 68,70,106
Denominators are 75,728,108
The GCF of 68,70,106 is 2 .
LCM of 75,728,108 is 491400.
The greatest common factor of 68/75,70/728,106/108 = [GCF of 68,70,106]/[LCM of 75,728,108]= 2/491400
Therefore, the GCF of 68/75,70/728,106/108 is 2/491400.
To find the highest common factor of 68,70,106, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 106 are 1, 2, 53, 106
The HCF of 68,70,106 is 2.
Lets's calculate GCF of 68,70,106
| 2 | 68, 70, 106 |
| 34, 35, 53 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 68,70,106 By Matching Biggest Common Factor Method
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 106
:1,2,53,106
Greatest Common Factor
We found the factors 68,70,106 . The biggest common factor number is the GCF number.
So the greatest common factor 68,70,106 is 2.
Lets's calculate LCM of 75,728,108
| 2 | 75, 728, 108 |
| 2 | 75, 364, 54 |
| 3 | 75, 182, 27 |
| 25, 182, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 25 x 182 x 9 = 491400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/491400
Therefore, the GCF of Fractions 68/75,70/728,106/108 is 2/491400
Least Common Multiple of 75,728,108 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 75,728,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,728,108) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(75,728,108) x common factors =1 x 12 = 12
LCM(75,728,108) = ( 75 × 728 × 108 ) / 12
LCM(75,728,108) = 5896800 / 12
LCM(75,728,108) = 491400
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 68/75, 70/728, 106/108
1. What is the HCF of 68,70,106?
The HCF of 68,70,106 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 68/75, 70/728, 106/108?
Answer: GCF of Numerators as per given numbers 68/75, 70/728, 106/108 is
GCF of Numerators i.e. for 68,70,106 is 2
LCM of denominators i.e. for 75,728,108 is 491400.
Thus, GCF of Fractions is 2/491400.Finally, GCF of Fractions for 68/75, 70/728, 106/108 is 2/491400.