Use our free GCF of Fractions Calculator tool to compute the GCF of 384/532, 653/164 i.e 1/21812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/532, 653/164.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 384/532,653/164
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 384/532,653/164, numerators are 384,653
Denominators are 532,164
The GCF of 384,653 is 1 .
LCM of 532,164 is 21812.
The greatest common factor of 384/532,653/164 = [GCF of 384,653]/[LCM of 532,164]= 1/21812
Therefore, the GCF of 384/532,653/164 is 1/21812.
To find the highest common factor of 384,653, we have to find the factors of both numbers and list the highest common factor.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The factors of 653 are 1, 653
The HCF of 384,653 is 1.
Lets's calculate GCF of 384,653
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Now, list down the factors of 653
:1,653
Greatest Common Factor
We found the factors 384,653 . The biggest common factor number is the GCF number.
So the greatest common factor 384,653 is 1.
Lets's calculate LCM of 532,164
2 | 532, 164 |
2 | 266, 82 |
133, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 133 x 41 = 21812
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21812
Therefore, the GCF of Fractions 384/532,653/164 is 1/21812
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 532,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(532,164) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(532,164) x common factors =4 x 1 = 4
LCM(532,164) = ( 532 × 164 ) / 4
LCM(532,164) = 87248 / 4
LCM(532,164) = 21812
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 384,653?
The HCF of 384,653 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 384/532, 653/164?
Answer: GCF of Numerators as per given numbers 384/532, 653/164 is
GCF of Numerators i.e. for 384,653 is 1
LCM of denominators i.e. for 532,164 is 21812.
Thus, GCF of Fractions is 1/21812.Finally, GCF of Fractions for 384/532, 653/164 is 1/21812.