GCF of 153/32, 5109/413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 153/32, 5109/413 i.e 3/13216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 153/32, 5109/413.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 153/32,5109/413?
Given fractions are 153/32,5109/413
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 153/32,5109/413, numerators are 153,5109
Denominators are 32,413
The GCF of 153,5109 is 3 .
LCM of 32,413 is 13216.
The greatest common factor of 153/32,5109/413 = [GCF of 153,5109]/[LCM of 32,413]= 3/13216
Therefore, the GCF of 153/32,5109/413 is 3/13216.
To find the highest common factor of 153,5109, 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 5109 are 1, 3, 13, 39, 131, 393, 1703, 5109
The HCF of 153,5109 is 3.
Lets's calculate GCF of 153,5109
| 3 | 153, 5109 |
| 51, 1703 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 153,5109 By Matching Biggest Common Factor Method
Now, list down the factors of 153
:1,3,9,17,51,153
Now, list down the factors of 5109
:1,3,13,39,131,393,1703,5109
Greatest Common Factor
We found the factors 153,5109 . The biggest common factor number is the GCF number.
So the greatest common factor 153,5109 is 3.
Lets's calculate LCM of 32,413
Given numbers has no common factors except 1. So, there LCM is their product i.e 13216
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/13216
Therefore, the GCF of Fractions 153/32,5109/413 is 3/13216
Least Common Multiple of 32,413 with GCF Formula
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 32,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(32,413) x common factors =1 x 1 = 1
LCM(32,413) = ( 32 × 413 ) / 1
LCM(32,413) = 13216 / 1
LCM(32,413) = 13216
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FAQs on GCF of Fractions of 153/32, 5109/413
1. What is the HCF of 153,5109?
The HCF of 153,5109 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 153/32, 5109/413?
Answer: GCF of Numerators as per given numbers 153/32, 5109/413 is
GCF of Numerators i.e. for 153,5109 is 3
LCM of denominators i.e. for 32,413 is 13216.
Thus, GCF of Fractions is 3/13216.Finally, GCF of Fractions for 153/32, 5109/413 is 3/13216.