Use our free GCF of Fractions Calculator tool to compute the GCF of 105/195, 189/362 i.e 21/70590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/195, 189/362.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 105/195,189/362
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 105/195,189/362, numerators are 105,189
Denominators are 195,362
The GCF of 105,189 is 21 .
LCM of 195,362 is 70590.
The greatest common factor of 105/195,189/362 = [GCF of 105,189]/[LCM of 195,362]= 21/70590
Therefore, the GCF of 105/195,189/362 is 21/70590.
To find the highest common factor of 105,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 105,189 is 21.
Lets's calculate GCF of 105,189
3 | 105, 189 |
7 | 35, 63 |
5, 9 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 105,189 . The biggest common factor number is the GCF number.
So the greatest common factor 105,189 is 21.
Lets's calculate LCM of 195,362
Given numbers has no common factors except 1. So, there LCM is their product i.e 70590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/70590
Therefore, the GCF of Fractions 105/195,189/362 is 21/70590
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 195,362 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(195,362) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(195,362) x common factors =1 x 1 = 1
LCM(195,362) = ( 195 × 362 ) / 1
LCM(195,362) = 70590 / 1
LCM(195,362) = 70590
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 105,189?
The HCF of 105,189 is 21
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 105/195, 189/362?
Answer: GCF of Numerators as per given numbers 105/195, 189/362 is
GCF of Numerators i.e. for 105,189 is 21
LCM of denominators i.e. for 195,362 is 70590.
Thus, GCF of Fractions is 21/70590.Finally, GCF of Fractions for 105/195, 189/362 is 21/70590.