Use our free GCF of Fractions Calculator tool to compute the GCF of 153/289, 321/320 i.e 3/92480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 153/289, 321/320.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 153/289,321/320
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 153/289,321/320, numerators are 153,321
Denominators are 289,320
The GCF of 153,321 is 3 .
LCM of 289,320 is 92480.
The greatest common factor of 153/289,321/320 = [GCF of 153,321]/[LCM of 289,320]= 3/92480
Therefore, the GCF of 153/289,321/320 is 3/92480.
To find the highest common factor of 153,321, we have to find the factors of both numbers and list the highest common factor.
The factors of 153 are 1, 3, 9, 17, 51, 153
The factors of 321 are 1, 3, 107, 321
The HCF of 153,321 is 3.
Lets's calculate GCF of 153,321
3 | 153, 321 |
51, 107 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 153
:1,3,9,17,51,153
Now, list down the factors of 321
:1,3,107,321
Greatest Common Factor
We found the factors 153,321 . The biggest common factor number is the GCF number.
So the greatest common factor 153,321 is 3.
Lets's calculate LCM of 289,320
Given numbers has no common factors except 1. So, there LCM is their product i.e 92480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/92480
Therefore, the GCF of Fractions 153/289,321/320 is 3/92480
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 289,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,320) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,320) x common factors =1 x 1 = 1
LCM(289,320) = ( 289 × 320 ) / 1
LCM(289,320) = 92480 / 1
LCM(289,320) = 92480
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 153,321?
The HCF of 153,321 is 3
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 153/289, 321/320?
Answer: GCF of Numerators as per given numbers 153/289, 321/320 is
GCF of Numerators i.e. for 153,321 is 3
LCM of denominators i.e. for 289,320 is 92480.
Thus, GCF of Fractions is 3/92480.Finally, GCF of Fractions for 153/289, 321/320 is 3/92480.