Use our free GCF of Fractions Calculator tool to compute the GCF of 213/669, 589/924 i.e 1/206052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/669, 589/924.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 213/669,589/924
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 213/669,589/924, numerators are 213,589
Denominators are 669,924
The GCF of 213,589 is 1 .
LCM of 669,924 is 206052.
The greatest common factor of 213/669,589/924 = [GCF of 213,589]/[LCM of 669,924]= 1/206052
Therefore, the GCF of 213/669,589/924 is 1/206052.
To find the highest common factor of 213,589, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 589 are 1, 19, 31, 589
The HCF of 213,589 is 1.
Lets's calculate GCF of 213,589
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 589
:1,19,31,589
Greatest Common Factor
We found the factors 213,589 . The biggest common factor number is the GCF number.
So the greatest common factor 213,589 is 1.
Lets's calculate LCM of 669,924
3 | 669, 924 |
223, 308 |
∴ So the LCM of the given numbers is 3 x 223 x 308 = 206052
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/206052
Therefore, the GCF of Fractions 213/669,589/924 is 1/206052
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 669,924 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(669,924) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(669,924) x common factors =3 x 1 = 3
LCM(669,924) = ( 669 × 924 ) / 3
LCM(669,924) = 618156 / 3
LCM(669,924) = 206052
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 213,589?
The HCF of 213,589 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 213/669, 589/924?
Answer: GCF of Numerators as per given numbers 213/669, 589/924 is
GCF of Numerators i.e. for 213,589 is 1
LCM of denominators i.e. for 669,924 is 206052.
Thus, GCF of Fractions is 1/206052.Finally, GCF of Fractions for 213/669, 589/924 is 1/206052.