Use our free GCF of Fractions Calculator tool to compute the GCF of 406/624, 334/984 i.e 2/25584 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/624, 334/984.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 406/624,334/984
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 406/624,334/984, numerators are 406,334
Denominators are 624,984
The GCF of 406,334 is 2 .
LCM of 624,984 is 25584.
The greatest common factor of 406/624,334/984 = [GCF of 406,334]/[LCM of 624,984]= 2/25584
Therefore, the GCF of 406/624,334/984 is 2/25584.
To find the highest common factor of 406,334, we have to find the factors of both numbers and list the highest common factor.
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The factors of 334 are 1, 2, 167, 334
The HCF of 406,334 is 2.
Lets's calculate GCF of 406,334
2 | 406, 334 |
203, 167 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Now, list down the factors of 334
:1,2,167,334
Greatest Common Factor
We found the factors 406,334 . The biggest common factor number is the GCF number.
So the greatest common factor 406,334 is 2.
Lets's calculate LCM of 624,984
2 | 624, 984 |
2 | 312, 492 |
2 | 156, 246 |
3 | 78, 123 |
26, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 26 x 41 = 25584
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/25584
Therefore, the GCF of Fractions 406/624,334/984 is 2/25584
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 624,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(624,984) = 24
common factors(in case of two or more numbers have common factors) = 1
GCF(624,984) x common factors =24 x 1 = 24
LCM(624,984) = ( 624 × 984 ) / 24
LCM(624,984) = 614016 / 24
LCM(624,984) = 25584
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 406,334?
The HCF of 406,334 is 2
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 406/624, 334/984?
Answer: GCF of Numerators as per given numbers 406/624, 334/984 is
GCF of Numerators i.e. for 406,334 is 2
LCM of denominators i.e. for 624,984 is 25584.
Thus, GCF of Fractions is 2/25584.Finally, GCF of Fractions for 406/624, 334/984 is 2/25584.