Use our free GCF of Fractions Calculator tool to compute the GCF of 13/85, 734/16, 870/340 i.e 1/1360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/85, 734/16, 870/340.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 13/85,734/16,870/340
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 13/85,734/16,870/340, numerators are 13,734,870
Denominators are 85,16,340
The GCF of 13,734,870 is 1 .
LCM of 85,16,340 is 1360.
The greatest common factor of 13/85,734/16,870/340 = [GCF of 13,734,870]/[LCM of 85,16,340]= 1/1360
Therefore, the GCF of 13/85,734/16,870/340 is 1/1360.
To find the highest common factor of 13,734,870, 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 734 are 1, 2, 367, 734
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 13,734,870 is 1.
Lets's calculate GCF of 13,734,870
∴ 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 734
:1,2,367,734
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 13,734,870 . The biggest common factor number is the GCF number.
So the greatest common factor 13,734,870 is 1.
Lets's calculate LCM of 85,16,340
2 | 85, 16, 340 |
2 | 85, 8, 170 |
5 | 85, 4, 85 |
17 | 17, 4, 17 |
1, 4, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 17 x 1 x 4 x 1 = 1360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1360
Therefore, the GCF of Fractions 13/85,734/16,870/340 is 1/1360
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 85,16,340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,16,340) = 1
common factors(in case of two or more numbers have common factors) = 340
GCF(85,16,340) x common factors =1 x 340 = 340
LCM(85,16,340) = ( 85 × 16 × 340 ) / 340
LCM(85,16,340) = 462400 / 340
LCM(85,16,340) = 1360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 13,734,870?
The HCF of 13,734,870 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 13/85, 734/16, 870/340?
Answer: GCF of Numerators as per given numbers 13/85, 734/16, 870/340 is
GCF of Numerators i.e. for 13,734,870 is 1
LCM of denominators i.e. for 85,16,340 is 1360.
Thus, GCF of Fractions is 1/1360.Finally, GCF of Fractions for 13/85, 734/16, 870/340 is 1/1360.