Use our free GCF of Fractions Calculator tool to compute the GCF of 212/954, 159/724 i.e 53/345348 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/954, 159/724.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 212/954,159/724
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 212/954,159/724, numerators are 212,159
Denominators are 954,724
The GCF of 212,159 is 53 .
LCM of 954,724 is 345348.
The greatest common factor of 212/954,159/724 = [GCF of 212,159]/[LCM of 954,724]= 53/345348
Therefore, the GCF of 212/954,159/724 is 53/345348.
To find the highest common factor of 212,159, we have to find the factors of both numbers and list the highest common factor.
The factors of 212 are 1, 2, 4, 53, 106, 212
The factors of 159 are 1, 3, 53, 159
The HCF of 212,159 is 53.
Lets's calculate GCF of 212,159
53 | 212, 159 |
4, 3 |
∴ So the GCF of the given numbers is 53 = 53
Now, list down the factors of 212
:1,2,4,53,106,212
Now, list down the factors of 159
:1,3,53,159
Greatest Common Factor
We found the factors 212,159 . The biggest common factor number is the GCF number.
So the greatest common factor 212,159 is 53.
Lets's calculate LCM of 954,724
2 | 954, 724 |
477, 362 |
∴ So the LCM of the given numbers is 2 x 477 x 362 = 345348
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 53/345348
Therefore, the GCF of Fractions 212/954,159/724 is 53/345348
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 954,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(954,724) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(954,724) x common factors =2 x 1 = 2
LCM(954,724) = ( 954 × 724 ) / 2
LCM(954,724) = 690696 / 2
LCM(954,724) = 345348
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 212,159?
The HCF of 212,159 is 53
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 212/954, 159/724?
Answer: GCF of Numerators as per given numbers 212/954, 159/724 is
GCF of Numerators i.e. for 212,159 is 53
LCM of denominators i.e. for 954,724 is 345348.
Thus, GCF of Fractions is 53/345348.Finally, GCF of Fractions for 212/954, 159/724 is 53/345348.