GCF of 654/114, 4209/6156
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 654/114, 4209/6156 i.e 3/6156 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/114, 4209/6156.
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 654/114,4209/6156?
Given fractions are 654/114,4209/6156
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 654/114,4209/6156, numerators are 654,4209
Denominators are 114,6156
The GCF of 654,4209 is 3 .
LCM of 114,6156 is 6156.
The greatest common factor of 654/114,4209/6156 = [GCF of 654,4209]/[LCM of 114,6156]= 3/6156
Therefore, the GCF of 654/114,4209/6156 is 3/6156.
To find the highest common factor of 654,4209, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 4209 are 1, 3, 23, 61, 69, 183, 1403, 4209
The HCF of 654,4209 is 3.
Lets's calculate GCF of 654,4209
| 3 | 654, 4209 |
| 218, 1403 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 654,4209 By Matching Biggest Common Factor Method
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 4209
:1,3,23,61,69,183,1403,4209
Greatest Common Factor
We found the factors 654,4209 . The biggest common factor number is the GCF number.
So the greatest common factor 654,4209 is 3.
Lets's calculate LCM of 114,6156
| 2 | 114, 6156 |
| 3 | 57, 3078 |
| 19 | 19, 1026 |
| 1, 54 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 1 x 54 = 6156
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/6156
Therefore, the GCF of Fractions 654/114,4209/6156 is 3/6156
Least Common Multiple of 114,6156 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 114,6156 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(114,6156) = 114
common factors(in case of two or more numbers have common factors) = 1
GCF(114,6156) x common factors =114 x 1 = 114
LCM(114,6156) = ( 114 × 6156 ) / 114
LCM(114,6156) = 701784 / 114
LCM(114,6156) = 6156
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FAQs on GCF of Fractions of 654/114, 4209/6156
1. What is the HCF of 654,4209?
The HCF of 654,4209 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 654/114, 4209/6156?
Answer: GCF of Numerators as per given numbers 654/114, 4209/6156 is
GCF of Numerators i.e. for 654,4209 is 3
LCM of denominators i.e. for 114,6156 is 6156.
Thus, GCF of Fractions is 3/6156.Finally, GCF of Fractions for 654/114, 4209/6156 is 3/6156.