Use our free GCF of Fractions Calculator tool to compute the GCF of 494/415, 608/221 i.e 38/91715 easily. The following is the detailed procedure to determine the greatest common factor of fractions 494/415, 608/221.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 494/415,608/221
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 494/415,608/221, numerators are 494,608
Denominators are 415,221
The GCF of 494,608 is 38 .
LCM of 415,221 is 91715.
The greatest common factor of 494/415,608/221 = [GCF of 494,608]/[LCM of 415,221]= 38/91715
Therefore, the GCF of 494/415,608/221 is 38/91715.
To find the highest common factor of 494,608, we have to find the factors of both numbers and list the highest common factor.
The factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494
The factors of 608 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608
The HCF of 494,608 is 38.
Lets's calculate GCF of 494,608
2 | 494, 608 |
19 | 247, 304 |
13, 16 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Now, list down the factors of 494
:1,2,13,19,26,38,247,494
Now, list down the factors of 608
:1,2,4,8,16,19,32,38,76,152,304,608
Greatest Common Factor
We found the factors 494,608 . The biggest common factor number is the GCF number.
So the greatest common factor 494,608 is 38.
Lets's calculate LCM of 415,221
Given numbers has no common factors except 1. So, there LCM is their product i.e 91715
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/91715
Therefore, the GCF of Fractions 494/415,608/221 is 38/91715
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 415,221 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(415,221) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(415,221) x common factors =1 x 1 = 1
LCM(415,221) = ( 415 × 221 ) / 1
LCM(415,221) = 91715 / 1
LCM(415,221) = 91715
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 494,608?
The HCF of 494,608 is 38
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 494/415, 608/221?
Answer: GCF of Numerators as per given numbers 494/415, 608/221 is
GCF of Numerators i.e. for 494,608 is 38
LCM of denominators i.e. for 415,221 is 91715.
Thus, GCF of Fractions is 38/91715.Finally, GCF of Fractions for 494/415, 608/221 is 38/91715.