Use our free GCF of Fractions Calculator tool to compute the GCF of 424/546, 564/226 i.e 4/61698 easily. The following is the detailed procedure to determine the greatest common factor of fractions 424/546, 564/226.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 424/546,564/226
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 424/546,564/226, numerators are 424,564
Denominators are 546,226
The GCF of 424,564 is 4 .
LCM of 546,226 is 61698.
The greatest common factor of 424/546,564/226 = [GCF of 424,564]/[LCM of 546,226]= 4/61698
Therefore, the GCF of 424/546,564/226 is 4/61698.
To find the highest common factor of 424,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 424,564 is 4.
Lets's calculate GCF of 424,564
2 | 424, 564 |
2 | 212, 282 |
106, 141 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 424
:1,2,4,8,53,106,212,424
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 424,564 . The biggest common factor number is the GCF number.
So the greatest common factor 424,564 is 4.
Lets's calculate LCM of 546,226
2 | 546, 226 |
273, 113 |
∴ So the LCM of the given numbers is 2 x 273 x 113 = 61698
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/61698
Therefore, the GCF of Fractions 424/546,564/226 is 4/61698
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 546,226 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,226) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(546,226) x common factors =2 x 1 = 2
LCM(546,226) = ( 546 × 226 ) / 2
LCM(546,226) = 123396 / 2
LCM(546,226) = 61698
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 424,564?
The HCF of 424,564 is 4
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 424/546, 564/226?
Answer: GCF of Numerators as per given numbers 424/546, 564/226 is
GCF of Numerators i.e. for 424,564 is 4
LCM of denominators i.e. for 546,226 is 61698.
Thus, GCF of Fractions is 4/61698.Finally, GCF of Fractions for 424/546, 564/226 is 4/61698.