Use our free GCF of Fractions Calculator tool to compute the GCF of 189/129, 945/914 i.e 189/117906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/129, 945/914.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 189/129,945/914
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 189/129,945/914, numerators are 189,945
Denominators are 129,914
The GCF of 189,945 is 189 .
LCM of 129,914 is 117906.
The greatest common factor of 189/129,945/914 = [GCF of 189,945]/[LCM of 129,914]= 189/117906
Therefore, the GCF of 189/129,945/914 is 189/117906.
To find the highest common factor of 189,945, we have to find the factors of both numbers and list the highest common factor.
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The HCF of 189,945 is 189.
Lets's calculate GCF of 189,945
3 | 189, 945 |
3 | 63, 315 |
3 | 21, 105 |
7 | 7, 35 |
1, 5 |
∴ So the GCF of the given numbers is 3 x 3 x 3 x 7 = 189
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Greatest Common Factor
We found the factors 189,945 . The biggest common factor number is the GCF number.
So the greatest common factor 189,945 is 189.
Lets's calculate LCM of 129,914
Given numbers has no common factors except 1. So, there LCM is their product i.e 117906
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 189/117906
Therefore, the GCF of Fractions 189/129,945/914 is 189/117906
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 129,914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(129,914) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(129,914) x common factors =1 x 1 = 1
LCM(129,914) = ( 129 × 914 ) / 1
LCM(129,914) = 117906 / 1
LCM(129,914) = 117906
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 189,945?
The HCF of 189,945 is 189
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 189/129, 945/914?
Answer: GCF of Numerators as per given numbers 189/129, 945/914 is
GCF of Numerators i.e. for 189,945 is 189
LCM of denominators i.e. for 129,914 is 117906.
Thus, GCF of Fractions is 189/117906.Finally, GCF of Fractions for 189/129, 945/914 is 189/117906.