Use our free GCF of Fractions Calculator tool to compute the GCF of 187/196, 616/188 i.e 11/9212 easily. The following is the detailed procedure to determine the greatest common factor of fractions 187/196, 616/188.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 187/196,616/188
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 187/196,616/188, numerators are 187,616
Denominators are 196,188
The GCF of 187,616 is 11 .
LCM of 196,188 is 9212.
The greatest common factor of 187/196,616/188 = [GCF of 187,616]/[LCM of 196,188]= 11/9212
Therefore, the GCF of 187/196,616/188 is 11/9212.
To find the highest common factor of 187,616, we have to find the factors of both numbers and list the highest common factor.
The factors of 187 are 1, 11, 17, 187
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The HCF of 187,616 is 11.
Lets's calculate GCF of 187,616
11 | 187, 616 |
17, 56 |
∴ So the GCF of the given numbers is 11 = 11
Now, list down the factors of 187
:1,11,17,187
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 187,616 . The biggest common factor number is the GCF number.
So the greatest common factor 187,616 is 11.
Lets's calculate LCM of 196,188
2 | 196, 188 |
2 | 98, 94 |
49, 47 |
∴ So the LCM of the given numbers is 2 x 2 x 49 x 47 = 9212
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/9212
Therefore, the GCF of Fractions 187/196,616/188 is 11/9212
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 196,188 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(196,188) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(196,188) x common factors =4 x 1 = 4
LCM(196,188) = ( 196 × 188 ) / 4
LCM(196,188) = 36848 / 4
LCM(196,188) = 9212
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 187,616?
The HCF of 187,616 is 11
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 187/196, 616/188?
Answer: GCF of Numerators as per given numbers 187/196, 616/188 is
GCF of Numerators i.e. for 187,616 is 11
LCM of denominators i.e. for 196,188 is 9212.
Thus, GCF of Fractions is 11/9212.Finally, GCF of Fractions for 187/196, 616/188 is 11/9212.