Use our free GCF of Fractions Calculator tool to compute the GCF of 13/10, 19/25, 689/10 i.e 1/50 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/10, 19/25, 689/10.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 13/10,19/25,689/10
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 13/10,19/25,689/10, numerators are 13,19,689
Denominators are 10,25,10
The GCF of 13,19,689 is 1 .
LCM of 10,25,10 is 50.
The greatest common factor of 13/10,19/25,689/10 = [GCF of 13,19,689]/[LCM of 10,25,10]= 1/50
Therefore, the GCF of 13/10,19/25,689/10 is 1/50.
To find the highest common factor of 13,19,689, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 19 are 1, 19
The factors of 689 are 1, 13, 53, 689
The HCF of 13,19,689 is 1.
Lets's calculate GCF of 13,19,689
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 13
:1,13
Now, list down the factors of 19
:1,19
Now, list down the factors of 689
:1,13,53,689
Greatest Common Factor
We found the factors 13,19,689 . The biggest common factor number is the GCF number.
So the greatest common factor 13,19,689 is 1.
Lets's calculate LCM of 10,25,10
2 | 10, 25, 10 |
5 | 5, 25, 5 |
1, 1, 5 |
∴ So the LCM of the given numbers is 2 x 5 x 1 x 1 x 5 = 50
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/50
Therefore, the GCF of Fractions 13/10,19/25,689/10 is 1/50
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 10,25,10 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,25,10) = 5
common factors(in case of two or more numbers have common factors) = 10
GCF(10,25,10) x common factors =5 x 10 = 50
LCM(10,25,10) = ( 10 × 25 × 10 ) / 50
LCM(10,25,10) = 2500 / 50
LCM(10,25,10) = 50
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 13,19,689?
The HCF of 13,19,689 is 1
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 13/10, 19/25, 689/10?
Answer: GCF of Numerators as per given numbers 13/10, 19/25, 689/10 is
GCF of Numerators i.e. for 13,19,689 is 1
LCM of denominators i.e. for 10,25,10 is 50.
Thus, GCF of Fractions is 1/50.Finally, GCF of Fractions for 13/10, 19/25, 689/10 is 1/50.