Use our free GCF of Fractions Calculator tool to compute the GCF of 4565/546, 6912/182 i.e 1/546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4565/546, 6912/182.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 4565/546,6912/182
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 4565/546,6912/182, numerators are 4565,6912
Denominators are 546,182
The GCF of 4565,6912 is 1 .
LCM of 546,182 is 546.
The greatest common factor of 4565/546,6912/182 = [GCF of 4565,6912]/[LCM of 546,182]= 1/546
Therefore, the GCF of 4565/546,6912/182 is 1/546.
To find the highest common factor of 4565,6912, we have to find the factors of both numbers and list the highest common factor.
The factors of 4565 are 1, 5, 11, 55, 83, 415, 913, 4565
The factors of 6912 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 576, 768, 864, 1152, 1728, 2304, 3456, 6912
The HCF of 4565,6912 is 1.
Lets's calculate GCF of 4565,6912
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 4565
:1,5,11,55,83,415,913,4565
Now, list down the factors of 6912
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,128,144,192,216,256,288,384,432,576,768,864,1152,1728,2304,3456,6912
Greatest Common Factor
We found the factors 4565,6912 . The biggest common factor number is the GCF number.
So the greatest common factor 4565,6912 is 1.
Lets's calculate LCM of 546,182
2 | 546, 182 |
7 | 273, 91 |
13 | 39, 13 |
3, 1 |
∴ So the LCM of the given numbers is 2 x 7 x 13 x 3 x 1 = 546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/546
Therefore, the GCF of Fractions 4565/546,6912/182 is 1/546
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 546,182 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,182) = 182
common factors(in case of two or more numbers have common factors) = 1
GCF(546,182) x common factors =182 x 1 = 182
LCM(546,182) = ( 546 × 182 ) / 182
LCM(546,182) = 99372 / 182
LCM(546,182) = 546
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 4565,6912?
The HCF of 4565,6912 is 1
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 4565/546, 6912/182?
Answer: GCF of Numerators as per given numbers 4565/546, 6912/182 is
GCF of Numerators i.e. for 4565,6912 is 1
LCM of denominators i.e. for 546,182 is 546.
Thus, GCF of Fractions is 1/546.Finally, GCF of Fractions for 4565/546, 6912/182 is 1/546.