GCF of 205/42, 205/723
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 205/42, 205/723 i.e 205/10122 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/42, 205/723.
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 205/42,205/723?
Given fractions are 205/42,205/723
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 205/42,205/723, numerators are 205,205
Denominators are 42,723
The GCF of 205,205 is 205 .
LCM of 42,723 is 10122.
The greatest common factor of 205/42,205/723 = [GCF of 205,205]/[LCM of 42,723]= 205/10122
Therefore, the GCF of 205/42,205/723 is 205/10122.
To find the highest common factor of 205,205, 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 205 are 1, 5, 41, 205
The HCF of 205,205 is 205.
Lets's calculate GCF of 205,205
| 5 | 205, 205 |
| 41 | 41, 41 |
| 1, 1 |
∴ So the GCF of the given numbers is 5 x 41 = 205
Greatest Common Factor of 205,205 By Matching Biggest Common Factor Method
Now, list down the factors of 205
:1,5,41,205
Now, list down the factors of 205
:1,5,41,205
Greatest Common Factor
We found the factors 205,205 . The biggest common factor number is the GCF number.
So the greatest common factor 205,205 is 205.
Lets's calculate LCM of 42,723
| 3 | 42, 723 |
| 14, 241 |
∴ So the LCM of the given numbers is 3 x 14 x 241 = 10122
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 205/10122
Therefore, the GCF of Fractions 205/42,205/723 is 205/10122
Least Common Multiple of 42,723 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 42,723 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,723) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(42,723) x common factors =3 x 1 = 3
LCM(42,723) = ( 42 × 723 ) / 3
LCM(42,723) = 30366 / 3
LCM(42,723) = 10122
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FAQs on GCF of Fractions of 205/42, 205/723
1. What is the HCF of 205,205?
The HCF of 205,205 is 205
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 205/42, 205/723?
Answer: GCF of Numerators as per given numbers 205/42, 205/723 is
GCF of Numerators i.e. for 205,205 is 205
LCM of denominators i.e. for 42,723 is 10122.
Thus, GCF of Fractions is 205/10122.Finally, GCF of Fractions for 205/42, 205/723 is 205/10122.