GCF of 414/201, 1863/538
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 414/201, 1863/538 i.e 207/108138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/201, 1863/538.
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 414/201,1863/538?
Given fractions are 414/201,1863/538
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 414/201,1863/538, numerators are 414,1863
Denominators are 201,538
The GCF of 414,1863 is 207 .
LCM of 201,538 is 108138.
The greatest common factor of 414/201,1863/538 = [GCF of 414,1863]/[LCM of 201,538]= 207/108138
Therefore, the GCF of 414/201,1863/538 is 207/108138.
To find the highest common factor of 414,1863, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 1863 are 1, 3, 9, 23, 27, 69, 81, 207, 621, 1863
The HCF of 414,1863 is 207.
Lets's calculate GCF of 414,1863
| 3 | 414, 1863 |
| 3 | 138, 621 |
| 23 | 46, 207 |
| 2, 9 |
∴ So the GCF of the given numbers is 3 x 3 x 23 = 207
Greatest Common Factor of 414,1863 By Matching Biggest Common Factor Method
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 1863
:1,3,9,23,27,69,81,207,621,1863
Greatest Common Factor
We found the factors 414,1863 . The biggest common factor number is the GCF number.
So the greatest common factor 414,1863 is 207.
Lets's calculate LCM of 201,538
Given numbers has no common factors except 1. So, there LCM is their product i.e 108138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 207/108138
Therefore, the GCF of Fractions 414/201,1863/538 is 207/108138
Least Common Multiple of 201,538 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 201,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(201,538) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(201,538) x common factors =1 x 1 = 1
LCM(201,538) = ( 201 × 538 ) / 1
LCM(201,538) = 108138 / 1
LCM(201,538) = 108138
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 414/201, 1863/538
1. What is the HCF of 414,1863?
The HCF of 414,1863 is 207
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 414/201, 1863/538?
Answer: GCF of Numerators as per given numbers 414/201, 1863/538 is
GCF of Numerators i.e. for 414,1863 is 207
LCM of denominators i.e. for 201,538 is 108138.
Thus, GCF of Fractions is 207/108138.Finally, GCF of Fractions for 414/201, 1863/538 is 207/108138.