Use our free GCF of Fractions Calculator tool to compute the GCF of 196/187, 686/646 i.e 98/7106 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/187, 686/646.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 196/187,686/646
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 196/187,686/646, numerators are 196,686
Denominators are 187,646
The GCF of 196,686 is 98 .
LCM of 187,646 is 7106.
The greatest common factor of 196/187,686/646 = [GCF of 196,686]/[LCM of 187,646]= 98/7106
Therefore, the GCF of 196/187,686/646 is 98/7106.
To find the highest common factor of 196,686, we have to find the factors of both numbers and list the highest common factor.
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 196,686 is 98.
Lets's calculate GCF of 196,686
2 | 196, 686 |
7 | 98, 343 |
7 | 14, 49 |
2, 7 |
∴ So the GCF of the given numbers is 2 x 7 x 7 = 98
Now, list down the factors of 196
:1,2,4,7,14,28,49,98,196
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 196,686 . The biggest common factor number is the GCF number.
So the greatest common factor 196,686 is 98.
Lets's calculate LCM of 187,646
17 | 187, 646 |
11, 38 |
∴ So the LCM of the given numbers is 17 x 11 x 38 = 7106
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 98/7106
Therefore, the GCF of Fractions 196/187,686/646 is 98/7106
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 187,646 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(187,646) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(187,646) x common factors =17 x 1 = 17
LCM(187,646) = ( 187 × 646 ) / 17
LCM(187,646) = 120802 / 17
LCM(187,646) = 7106
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 196,686?
The HCF of 196,686 is 98
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 196/187, 686/646?
Answer: GCF of Numerators as per given numbers 196/187, 686/646 is
GCF of Numerators i.e. for 196,686 is 98
LCM of denominators i.e. for 187,646 is 7106.
Thus, GCF of Fractions is 98/7106.Finally, GCF of Fractions for 196/187, 686/646 is 98/7106.