GCF of 8209/162, 9060/312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8209/162, 9060/312 i.e 1/8424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8209/162, 9060/312.
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 8209/162,9060/312?
Given fractions are 8209/162,9060/312
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 8209/162,9060/312, numerators are 8209,9060
Denominators are 162,312
The GCF of 8209,9060 is 1 .
LCM of 162,312 is 8424.
The greatest common factor of 8209/162,9060/312 = [GCF of 8209,9060]/[LCM of 162,312]= 1/8424
Therefore, the GCF of 8209/162,9060/312 is 1/8424.
To find the highest common factor of 8209,9060, we have to find the factors of both numbers and list the highest common factor.
The factors of 8209 are 1, 8209
The factors of 9060 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 151, 302, 453, 604, 755, 906, 1510, 1812, 2265, 3020, 4530, 9060
The HCF of 8209,9060 is 1.
Lets's calculate GCF of 8209,9060
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8209,9060 By Matching Biggest Common Factor Method
Now, list down the factors of 8209
:1,8209
Now, list down the factors of 9060
:1,2,3,4,5,6,10,12,15,20,30,60,151,302,453,604,755,906,1510,1812,2265,3020,4530,9060
Greatest Common Factor
We found the factors 8209,9060 . The biggest common factor number is the GCF number.
So the greatest common factor 8209,9060 is 1.
Lets's calculate LCM of 162,312
| 2 | 162, 312 |
| 3 | 81, 156 |
| 27, 52 |
∴ So the LCM of the given numbers is 2 x 3 x 27 x 52 = 8424
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8424
Therefore, the GCF of Fractions 8209/162,9060/312 is 1/8424
Least Common Multiple of 162,312 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 162,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(162,312) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(162,312) x common factors =6 x 1 = 6
LCM(162,312) = ( 162 × 312 ) / 6
LCM(162,312) = 50544 / 6
LCM(162,312) = 8424
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FAQs on GCF of Fractions of 8209/162, 9060/312
1. What is the HCF of 8209,9060?
The HCF of 8209,9060 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 8209/162, 9060/312?
Answer: GCF of Numerators as per given numbers 8209/162, 9060/312 is
GCF of Numerators i.e. for 8209,9060 is 1
LCM of denominators i.e. for 162,312 is 8424.
Thus, GCF of Fractions is 1/8424.Finally, GCF of Fractions for 8209/162, 9060/312 is 1/8424.