Use our free GCF of Fractions Calculator tool to compute the GCF of 19/17, 235/32, 208/820 i.e 1/111520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/17, 235/32, 208/820.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 19/17,235/32,208/820
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 19/17,235/32,208/820, numerators are 19,235,208
Denominators are 17,32,820
The GCF of 19,235,208 is 1 .
LCM of 17,32,820 is 111520.
The greatest common factor of 19/17,235/32,208/820 = [GCF of 19,235,208]/[LCM of 17,32,820]= 1/111520
Therefore, the GCF of 19/17,235/32,208/820 is 1/111520.
To find the highest common factor of 19,235,208, we have to find the factors of both numbers and list the highest common factor.
The factors of 19 are 1, 19
The factors of 235 are 1, 5, 47, 235
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The HCF of 19,235,208 is 1.
Lets's calculate GCF of 19,235,208
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 19
:1,19
Now, list down the factors of 235
:1,5,47,235
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Greatest Common Factor
We found the factors 19,235,208 . The biggest common factor number is the GCF number.
So the greatest common factor 19,235,208 is 1.
Lets's calculate LCM of 17,32,820
2 | 17, 32, 820 |
2 | 17, 16, 410 |
17, 8, 205 |
∴ So the LCM of the given numbers is 2 x 2 x 17 x 8 x 205 = 111520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/111520
Therefore, the GCF of Fractions 19/17,235/32,208/820 is 1/111520
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 17,32,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,32,820) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(17,32,820) x common factors =1 x 4 = 4
LCM(17,32,820) = ( 17 × 32 × 820 ) / 4
LCM(17,32,820) = 446080 / 4
LCM(17,32,820) = 111520
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 19,235,208?
The HCF of 19,235,208 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 19/17, 235/32, 208/820?
Answer: GCF of Numerators as per given numbers 19/17, 235/32, 208/820 is
GCF of Numerators i.e. for 19,235,208 is 1
LCM of denominators i.e. for 17,32,820 is 111520.
Thus, GCF of Fractions is 1/111520.Finally, GCF of Fractions for 19/17, 235/32, 208/820 is 1/111520.