GCF of 205/40, 563/14, 546/38
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 205/40, 563/14, 546/38 i.e 1/5320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/40, 563/14, 546/38.
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 205/40,563/14,546/38?
Given fractions are 205/40,563/14,546/38
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 205/40,563/14,546/38, numerators are 205,563,546
Denominators are 40,14,38
The GCF of 205,563,546 is 1 .
LCM of 40,14,38 is 5320.
The greatest common factor of 205/40,563/14,546/38 = [GCF of 205,563,546]/[LCM of 40,14,38]= 1/5320
Therefore, the GCF of 205/40,563/14,546/38 is 1/5320.
To find the highest common factor of 205,563,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 205 are 1, 5, 41, 205
The factors of 563 are 1, 563
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 205,563,546 is 1.
Lets's calculate GCF of 205,563,546
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 205,563,546 By Matching Biggest Common Factor Method
Now, list down the factors of 205
:1,5,41,205
Now, list down the factors of 563
:1,563
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 205,563,546 . The biggest common factor number is the GCF number.
So the greatest common factor 205,563,546 is 1.
Lets's calculate LCM of 40,14,38
| 2 | 40, 14, 38 |
| 20, 7, 19 |
∴ So the LCM of the given numbers is 2 x 20 x 7 x 19 = 5320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5320
Therefore, the GCF of Fractions 205/40,563/14,546/38 is 1/5320
Least Common Multiple of 40,14,38 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 40,14,38 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,14,38) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(40,14,38) x common factors =2 x 2 = 4
LCM(40,14,38) = ( 40 × 14 × 38 ) / 4
LCM(40,14,38) = 21280 / 4
LCM(40,14,38) = 5320
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FAQs on GCF of Fractions of 205/40, 563/14, 546/38
1. What is the HCF of 205,563,546?
The HCF of 205,563,546 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 205/40, 563/14, 546/38?
Answer: GCF of Numerators as per given numbers 205/40, 563/14, 546/38 is
GCF of Numerators i.e. for 205,563,546 is 1
LCM of denominators i.e. for 40,14,38 is 5320.
Thus, GCF of Fractions is 1/5320.Finally, GCF of Fractions for 205/40, 563/14, 546/38 is 1/5320.