Use our free GCF of Fractions Calculator tool to compute the GCF of 189/914, 117/840 i.e 9/383880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/914, 117/840.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 189/914,117/840
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 189/914,117/840, numerators are 189,117
Denominators are 914,840
The GCF of 189,117 is 9 .
LCM of 914,840 is 383880.
The greatest common factor of 189/914,117/840 = [GCF of 189,117]/[LCM of 914,840]= 9/383880
Therefore, the GCF of 189/914,117/840 is 9/383880.
To find the highest common factor of 189,117, 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 117 are 1, 3, 9, 13, 39, 117
The HCF of 189,117 is 9.
Lets's calculate GCF of 189,117
3 | 189, 117 |
3 | 63, 39 |
21, 13 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 117
:1,3,9,13,39,117
Greatest Common Factor
We found the factors 189,117 . The biggest common factor number is the GCF number.
So the greatest common factor 189,117 is 9.
Lets's calculate LCM of 914,840
2 | 914, 840 |
457, 420 |
∴ So the LCM of the given numbers is 2 x 457 x 420 = 383880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/383880
Therefore, the GCF of Fractions 189/914,117/840 is 9/383880
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 914,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(914,840) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(914,840) x common factors =2 x 1 = 2
LCM(914,840) = ( 914 × 840 ) / 2
LCM(914,840) = 767760 / 2
LCM(914,840) = 383880
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 189,117?
The HCF of 189,117 is 9
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 189/914, 117/840?
Answer: GCF of Numerators as per given numbers 189/914, 117/840 is
GCF of Numerators i.e. for 189,117 is 9
LCM of denominators i.e. for 914,840 is 383880.
Thus, GCF of Fractions is 9/383880.Finally, GCF of Fractions for 189/914, 117/840 is 9/383880.