Use our free GCF of Fractions Calculator tool to compute the GCF of 172/130, 644/259 i.e 4/33670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 172/130, 644/259.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 172/130,644/259
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 172/130,644/259, numerators are 172,644
Denominators are 130,259
The GCF of 172,644 is 4 .
LCM of 130,259 is 33670.
The greatest common factor of 172/130,644/259 = [GCF of 172,644]/[LCM of 130,259]= 4/33670
Therefore, the GCF of 172/130,644/259 is 4/33670.
To find the highest common factor of 172,644, we have to find the factors of both numbers and list the highest common factor.
The factors of 172 are 1, 2, 4, 43, 86, 172
The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644
The HCF of 172,644 is 4.
Lets's calculate GCF of 172,644
2 | 172, 644 |
2 | 86, 322 |
43, 161 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 172
:1,2,4,43,86,172
Now, list down the factors of 644
:1,2,4,7,14,23,28,46,92,161,322,644
Greatest Common Factor
We found the factors 172,644 . The biggest common factor number is the GCF number.
So the greatest common factor 172,644 is 4.
Lets's calculate LCM of 130,259
Given numbers has no common factors except 1. So, there LCM is their product i.e 33670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/33670
Therefore, the GCF of Fractions 172/130,644/259 is 4/33670
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 130,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(130,259) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(130,259) x common factors =1 x 1 = 1
LCM(130,259) = ( 130 × 259 ) / 1
LCM(130,259) = 33670 / 1
LCM(130,259) = 33670
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 172,644?
The HCF of 172,644 is 4
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 172/130, 644/259?
Answer: GCF of Numerators as per given numbers 172/130, 644/259 is
GCF of Numerators i.e. for 172,644 is 4
LCM of denominators i.e. for 130,259 is 33670.
Thus, GCF of Fractions is 4/33670.Finally, GCF of Fractions for 172/130, 644/259 is 4/33670.