GCF of 405/42, 206/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 405/42, 206/546 i.e 1/546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 405/42, 206/546.
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 405/42,206/546?
Given fractions are 405/42,206/546
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 405/42,206/546, numerators are 405,206
Denominators are 42,546
The GCF of 405,206 is 1 .
LCM of 42,546 is 546.
The greatest common factor of 405/42,206/546 = [GCF of 405,206]/[LCM of 42,546]= 1/546
Therefore, the GCF of 405/42,206/546 is 1/546.
To find the highest common factor of 405,206, we have to find the factors of both numbers and list the highest common factor.
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The factors of 206 are 1, 2, 103, 206
The HCF of 405,206 is 1.
Lets's calculate GCF of 405,206
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 405,206 By Matching Biggest Common Factor Method
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Now, list down the factors of 206
:1,2,103,206
Greatest Common Factor
We found the factors 405,206 . The biggest common factor number is the GCF number.
So the greatest common factor 405,206 is 1.
Lets's calculate LCM of 42,546
| 2 | 42, 546 |
| 3 | 21, 273 |
| 7 | 7, 91 |
| 1, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1 x 13 = 546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/546
Therefore, the GCF of Fractions 405/42,206/546 is 1/546
Least Common Multiple of 42,546 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 42,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,546) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(42,546) x common factors =42 x 1 = 42
LCM(42,546) = ( 42 × 546 ) / 42
LCM(42,546) = 22932 / 42
LCM(42,546) = 546
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 405/42, 206/546
1. What is the HCF of 405,206?
The HCF of 405,206 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 405/42, 206/546?
Answer: GCF of Numerators as per given numbers 405/42, 206/546 is
GCF of Numerators i.e. for 405,206 is 1
LCM of denominators i.e. for 42,546 is 546.
Thus, GCF of Fractions is 1/546.Finally, GCF of Fractions for 405/42, 206/546 is 1/546.