Use our free GCF of Fractions Calculator tool to compute the GCF of 70/404, 65/7878 i.e 5/15756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/404, 65/7878.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 70/404,65/7878
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 70/404,65/7878, numerators are 70,65
Denominators are 404,7878
The GCF of 70,65 is 5 .
LCM of 404,7878 is 15756.
The greatest common factor of 70/404,65/7878 = [GCF of 70,65]/[LCM of 404,7878]= 5/15756
Therefore, the GCF of 70/404,65/7878 is 5/15756.
To find the highest common factor of 70,65, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 65 are 1, 5, 13, 65
The HCF of 70,65 is 5.
Lets's calculate GCF of 70,65
5 | 70, 65 |
14, 13 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 65
:1,5,13,65
Greatest Common Factor
We found the factors 70,65 . The biggest common factor number is the GCF number.
So the greatest common factor 70,65 is 5.
Lets's calculate LCM of 404,7878
2 | 404, 7878 |
101 | 202, 3939 |
2, 39 |
∴ So the LCM of the given numbers is 2 x 101 x 2 x 39 = 15756
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/15756
Therefore, the GCF of Fractions 70/404,65/7878 is 5/15756
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 404,7878 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(404,7878) = 202
common factors(in case of two or more numbers have common factors) = 1
GCF(404,7878) x common factors =202 x 1 = 202
LCM(404,7878) = ( 404 × 7878 ) / 202
LCM(404,7878) = 3182712 / 202
LCM(404,7878) = 15756
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 70,65?
The HCF of 70,65 is 5
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 70/404, 65/7878?
Answer: GCF of Numerators as per given numbers 70/404, 65/7878 is
GCF of Numerators i.e. for 70,65 is 5
LCM of denominators i.e. for 404,7878 is 15756.
Thus, GCF of Fractions is 5/15756.Finally, GCF of Fractions for 70/404, 65/7878 is 5/15756.