GCF of 8184/137, 5109/2914
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8184/137, 5109/2914 i.e 3/399218 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8184/137, 5109/2914.
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 8184/137,5109/2914?
Given fractions are 8184/137,5109/2914
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 8184/137,5109/2914, numerators are 8184,5109
Denominators are 137,2914
The GCF of 8184,5109 is 3 .
LCM of 137,2914 is 399218.
The greatest common factor of 8184/137,5109/2914 = [GCF of 8184,5109]/[LCM of 137,2914]= 3/399218
Therefore, the GCF of 8184/137,5109/2914 is 3/399218.
To find the highest common factor of 8184,5109, we have to find the factors of both numbers and list the highest common factor.
The factors of 8184 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 31, 33, 44, 62, 66, 88, 93, 124, 132, 186, 248, 264, 341, 372, 682, 744, 1023, 1364, 2046, 2728, 4092, 8184
The factors of 5109 are 1, 3, 13, 39, 131, 393, 1703, 5109
The HCF of 8184,5109 is 3.
Lets's calculate GCF of 8184,5109
| 3 | 8184, 5109 |
| 2728, 1703 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8184,5109 By Matching Biggest Common Factor Method
Now, list down the factors of 8184
:1,2,3,4,6,8,11,12,22,24,31,33,44,62,66,88,93,124,132,186,248,264,341,372,682,744,1023,1364,2046,2728,4092,8184
Now, list down the factors of 5109
:1,3,13,39,131,393,1703,5109
Greatest Common Factor
We found the factors 8184,5109 . The biggest common factor number is the GCF number.
So the greatest common factor 8184,5109 is 3.
Lets's calculate LCM of 137,2914
Given numbers has no common factors except 1. So, there LCM is their product i.e 399218
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/399218
Therefore, the GCF of Fractions 8184/137,5109/2914 is 3/399218
Least Common Multiple of 137,2914 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 137,2914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(137,2914) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(137,2914) x common factors =1 x 1 = 1
LCM(137,2914) = ( 137 × 2914 ) / 1
LCM(137,2914) = 399218 / 1
LCM(137,2914) = 399218
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 8184/137, 5109/2914
1. What is the HCF of 8184,5109?
The HCF of 8184,5109 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 8184/137, 5109/2914?
Answer: GCF of Numerators as per given numbers 8184/137, 5109/2914 is
GCF of Numerators i.e. for 8184,5109 is 3
LCM of denominators i.e. for 137,2914 is 399218.
Thus, GCF of Fractions is 3/399218.Finally, GCF of Fractions for 8184/137, 5109/2914 is 3/399218.