Use our free GCF of Fractions Calculator tool to compute the GCF of 21/145, 69/4395 i.e 3/127455 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/145, 69/4395.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/145,69/4395
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 21/145,69/4395, numerators are 21,69
Denominators are 145,4395
The GCF of 21,69 is 3 .
LCM of 145,4395 is 127455.
The greatest common factor of 21/145,69/4395 = [GCF of 21,69]/[LCM of 145,4395]= 3/127455
Therefore, the GCF of 21/145,69/4395 is 3/127455.
To find the highest common factor of 21,69, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 69 are 1, 3, 23, 69
The HCF of 21,69 is 3.
Lets's calculate GCF of 21,69
3 | 21, 69 |
7, 23 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 69
:1,3,23,69
Greatest Common Factor
We found the factors 21,69 . The biggest common factor number is the GCF number.
So the greatest common factor 21,69 is 3.
Lets's calculate LCM of 145,4395
5 | 145, 4395 |
29, 879 |
∴ So the LCM of the given numbers is 5 x 29 x 879 = 127455
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/127455
Therefore, the GCF of Fractions 21/145,69/4395 is 3/127455
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 145,4395 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(145,4395) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(145,4395) x common factors =5 x 1 = 5
LCM(145,4395) = ( 145 × 4395 ) / 5
LCM(145,4395) = 637275 / 5
LCM(145,4395) = 127455
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,69?
The HCF of 21,69 is 3
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 21/145, 69/4395?
Answer: GCF of Numerators as per given numbers 21/145, 69/4395 is
GCF of Numerators i.e. for 21,69 is 3
LCM of denominators i.e. for 145,4395 is 127455.
Thus, GCF of Fractions is 3/127455.Finally, GCF of Fractions for 21/145, 69/4395 is 3/127455.