Use our free GCF of Fractions Calculator tool to compute the GCF of 65/69, 80/74, 145/74 i.e 5/5106 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/69, 80/74, 145/74.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/69,80/74,145/74
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 65/69,80/74,145/74, numerators are 65,80,145
Denominators are 69,74,74
The GCF of 65,80,145 is 5 .
LCM of 69,74,74 is 5106.
The greatest common factor of 65/69,80/74,145/74 = [GCF of 65,80,145]/[LCM of 69,74,74]= 5/5106
Therefore, the GCF of 65/69,80/74,145/74 is 5/5106.
To find the highest common factor of 65,80,145, we have to find the factors of both numbers and list the highest common factor.
The factors of 65 are 1, 5, 13, 65
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 145 are 1, 5, 29, 145
The HCF of 65,80,145 is 5.
Lets's calculate GCF of 65,80,145
5 | 65, 80, 145 |
13, 16, 29 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 145
:1,5,29,145
Greatest Common Factor
We found the factors 65,80,145 . The biggest common factor number is the GCF number.
So the greatest common factor 65,80,145 is 5.
Lets's calculate LCM of 69,74,74
2 | 69, 74, 74 |
37 | 69, 37, 37 |
69, 1, 1 |
∴ So the LCM of the given numbers is 2 x 37 x 69 x 1 x 1 = 5106
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/5106
Therefore, the GCF of Fractions 65/69,80/74,145/74 is 5/5106
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 69,74,74 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,74,74) = 1
common factors(in case of two or more numbers have common factors) = 74
GCF(69,74,74) x common factors =1 x 74 = 74
LCM(69,74,74) = ( 69 × 74 × 74 ) / 74
LCM(69,74,74) = 377844 / 74
LCM(69,74,74) = 5106
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 65,80,145?
The HCF of 65,80,145 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 65/69, 80/74, 145/74?
Answer: GCF of Numerators as per given numbers 65/69, 80/74, 145/74 is
GCF of Numerators i.e. for 65,80,145 is 5
LCM of denominators i.e. for 69,74,74 is 5106.
Thus, GCF of Fractions is 5/5106.Finally, GCF of Fractions for 65/69, 80/74, 145/74 is 5/5106.