Use our free GCF of Fractions Calculator tool to compute the GCF of 574/409, 176/505 i.e 2/206545 easily. The following is the detailed procedure to determine the greatest common factor of fractions 574/409, 176/505.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 574/409,176/505
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 574/409,176/505, numerators are 574,176
Denominators are 409,505
The GCF of 574,176 is 2 .
LCM of 409,505 is 206545.
The greatest common factor of 574/409,176/505 = [GCF of 574,176]/[LCM of 409,505]= 2/206545
Therefore, the GCF of 574/409,176/505 is 2/206545.
To find the highest common factor of 574,176, we have to find the factors of both numbers and list the highest common factor.
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
The HCF of 574,176 is 2.
Lets's calculate GCF of 574,176
2 | 574, 176 |
287, 88 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Now, list down the factors of 176
:1,2,4,8,11,16,22,44,88,176
Greatest Common Factor
We found the factors 574,176 . The biggest common factor number is the GCF number.
So the greatest common factor 574,176 is 2.
Lets's calculate LCM of 409,505
Given numbers has no common factors except 1. So, there LCM is their product i.e 206545
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/206545
Therefore, the GCF of Fractions 574/409,176/505 is 2/206545
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 409,505 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,505) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,505) x common factors =1 x 1 = 1
LCM(409,505) = ( 409 × 505 ) / 1
LCM(409,505) = 206545 / 1
LCM(409,505) = 206545
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 574,176?
The HCF of 574,176 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 574/409, 176/505?
Answer: GCF of Numerators as per given numbers 574/409, 176/505 is
GCF of Numerators i.e. for 574,176 is 2
LCM of denominators i.e. for 409,505 is 206545.
Thus, GCF of Fractions is 2/206545.Finally, GCF of Fractions for 574/409, 176/505 is 2/206545.