Use our free GCF of Fractions Calculator tool to compute the GCF of 546/206, 320/462 i.e 2/47586 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/206, 320/462.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 546/206,320/462
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 546/206,320/462, numerators are 546,320
Denominators are 206,462
The GCF of 546,320 is 2 .
LCM of 206,462 is 47586.
The greatest common factor of 546/206,320/462 = [GCF of 546,320]/[LCM of 206,462]= 2/47586
Therefore, the GCF of 546/206,320/462 is 2/47586.
To find the highest common factor of 546,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 546,320 is 2.
Lets's calculate GCF of 546,320
2 | 546, 320 |
273, 160 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 546,320 . The biggest common factor number is the GCF number.
So the greatest common factor 546,320 is 2.
Lets's calculate LCM of 206,462
2 | 206, 462 |
103, 231 |
∴ So the LCM of the given numbers is 2 x 103 x 231 = 47586
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/47586
Therefore, the GCF of Fractions 546/206,320/462 is 2/47586
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 206,462 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(206,462) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(206,462) x common factors =2 x 1 = 2
LCM(206,462) = ( 206 × 462 ) / 2
LCM(206,462) = 95172 / 2
LCM(206,462) = 47586
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 546,320?
The HCF of 546,320 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 546/206, 320/462?
Answer: GCF of Numerators as per given numbers 546/206, 320/462 is
GCF of Numerators i.e. for 546,320 is 2
LCM of denominators i.e. for 206,462 is 47586.
Thus, GCF of Fractions is 2/47586.Finally, GCF of Fractions for 546/206, 320/462 is 2/47586.