Use our free GCF of Fractions Calculator tool to compute the GCF of 564/406, 326/372 i.e 2/75516 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/406, 326/372.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 564/406,326/372
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 564/406,326/372, numerators are 564,326
Denominators are 406,372
The GCF of 564,326 is 2 .
LCM of 406,372 is 75516.
The greatest common factor of 564/406,326/372 = [GCF of 564,326]/[LCM of 406,372]= 2/75516
Therefore, the GCF of 564/406,326/372 is 2/75516.
To find the highest common factor of 564,326, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 326 are 1, 2, 163, 326
The HCF of 564,326 is 2.
Lets's calculate GCF of 564,326
2 | 564, 326 |
282, 163 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 326
:1,2,163,326
Greatest Common Factor
We found the factors 564,326 . The biggest common factor number is the GCF number.
So the greatest common factor 564,326 is 2.
Lets's calculate LCM of 406,372
2 | 406, 372 |
203, 186 |
∴ So the LCM of the given numbers is 2 x 203 x 186 = 75516
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/75516
Therefore, the GCF of Fractions 564/406,326/372 is 2/75516
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 406,372 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,372) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,372) x common factors =2 x 1 = 2
LCM(406,372) = ( 406 × 372 ) / 2
LCM(406,372) = 151032 / 2
LCM(406,372) = 75516
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 564,326?
The HCF of 564,326 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 564/406, 326/372?
Answer: GCF of Numerators as per given numbers 564/406, 326/372 is
GCF of Numerators i.e. for 564,326 is 2
LCM of denominators i.e. for 406,372 is 75516.
Thus, GCF of Fractions is 2/75516.Finally, GCF of Fractions for 564/406, 326/372 is 2/75516.