Use our free GCF of Fractions Calculator tool to compute the GCF of 671/312, 829/556 i.e 1/43368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 671/312, 829/556.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 671/312,829/556
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 671/312,829/556, numerators are 671,829
Denominators are 312,556
The GCF of 671,829 is 1 .
LCM of 312,556 is 43368.
The greatest common factor of 671/312,829/556 = [GCF of 671,829]/[LCM of 312,556]= 1/43368
Therefore, the GCF of 671/312,829/556 is 1/43368.
To find the highest common factor of 671,829, we have to find the factors of both numbers and list the highest common factor.
The factors of 671 are 1, 11, 61, 671
The factors of 829 are 1, 829
The HCF of 671,829 is 1.
Lets's calculate GCF of 671,829
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 671
:1,11,61,671
Now, list down the factors of 829
:1,829
Greatest Common Factor
We found the factors 671,829 . The biggest common factor number is the GCF number.
So the greatest common factor 671,829 is 1.
Lets's calculate LCM of 312,556
2 | 312, 556 |
2 | 156, 278 |
78, 139 |
∴ So the LCM of the given numbers is 2 x 2 x 78 x 139 = 43368
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43368
Therefore, the GCF of Fractions 671/312,829/556 is 1/43368
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 312,556 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,556) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(312,556) x common factors =4 x 1 = 4
LCM(312,556) = ( 312 × 556 ) / 4
LCM(312,556) = 173472 / 4
LCM(312,556) = 43368
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 671,829?
The HCF of 671,829 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 671/312, 829/556?
Answer: GCF of Numerators as per given numbers 671/312, 829/556 is
GCF of Numerators i.e. for 671,829 is 1
LCM of denominators i.e. for 312,556 is 43368.
Thus, GCF of Fractions is 1/43368.Finally, GCF of Fractions for 671/312, 829/556 is 1/43368.