Use our free GCF of Fractions Calculator tool to compute the GCF of 169/309, 820/177 i.e 1/18231 easily. The following is the detailed procedure to determine the greatest common factor of fractions 169/309, 820/177.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 169/309,820/177
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 169/309,820/177, numerators are 169,820
Denominators are 309,177
The GCF of 169,820 is 1 .
LCM of 309,177 is 18231.
The greatest common factor of 169/309,820/177 = [GCF of 169,820]/[LCM of 309,177]= 1/18231
Therefore, the GCF of 169/309,820/177 is 1/18231.
To find the highest common factor of 169,820, we have to find the factors of both numbers and list the highest common factor.
The factors of 169 are 1, 13, 169
The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
The HCF of 169,820 is 1.
Lets's calculate GCF of 169,820
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 169
:1,13,169
Now, list down the factors of 820
:1,2,4,5,10,20,41,82,164,205,410,820
Greatest Common Factor
We found the factors 169,820 . The biggest common factor number is the GCF number.
So the greatest common factor 169,820 is 1.
Lets's calculate LCM of 309,177
3 | 309, 177 |
103, 59 |
∴ So the LCM of the given numbers is 3 x 103 x 59 = 18231
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18231
Therefore, the GCF of Fractions 169/309,820/177 is 1/18231
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 309,177 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,177) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,177) x common factors =3 x 1 = 3
LCM(309,177) = ( 309 × 177 ) / 3
LCM(309,177) = 54693 / 3
LCM(309,177) = 18231
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 169,820?
The HCF of 169,820 is 1
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 169/309, 820/177?
Answer: GCF of Numerators as per given numbers 169/309, 820/177 is
GCF of Numerators i.e. for 169,820 is 1
LCM of denominators i.e. for 309,177 is 18231.
Thus, GCF of Fractions is 1/18231.Finally, GCF of Fractions for 169/309, 820/177 is 1/18231.