Use our free GCF of Fractions Calculator tool to compute the GCF of 670/399, 975/441 i.e 5/8379 easily. The following is the detailed procedure to determine the greatest common factor of fractions 670/399, 975/441.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 670/399,975/441
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 670/399,975/441, numerators are 670,975
Denominators are 399,441
The GCF of 670,975 is 5 .
LCM of 399,441 is 8379.
The greatest common factor of 670/399,975/441 = [GCF of 670,975]/[LCM of 399,441]= 5/8379
Therefore, the GCF of 670/399,975/441 is 5/8379.
To find the highest common factor of 670,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 670,975 is 5.
Lets's calculate GCF of 670,975
5 | 670, 975 |
134, 195 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 670
:1,2,5,10,67,134,335,670
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 670,975 . The biggest common factor number is the GCF number.
So the greatest common factor 670,975 is 5.
Lets's calculate LCM of 399,441
3 | 399, 441 |
7 | 133, 147 |
19, 21 |
∴ So the LCM of the given numbers is 3 x 7 x 19 x 21 = 8379
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/8379
Therefore, the GCF of Fractions 670/399,975/441 is 5/8379
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 399,441 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(399,441) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(399,441) x common factors =21 x 1 = 21
LCM(399,441) = ( 399 × 441 ) / 21
LCM(399,441) = 175959 / 21
LCM(399,441) = 8379
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 670,975?
The HCF of 670,975 is 5
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 670/399, 975/441?
Answer: GCF of Numerators as per given numbers 670/399, 975/441 is
GCF of Numerators i.e. for 670,975 is 5
LCM of denominators i.e. for 399,441 is 8379.
Thus, GCF of Fractions is 5/8379.Finally, GCF of Fractions for 670/399, 975/441 is 5/8379.