GCF of 1205/300, 1199/565
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1205/300, 1199/565 i.e 1/33900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1205/300, 1199/565.
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 1205/300,1199/565?
Given fractions are 1205/300,1199/565
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 1205/300,1199/565, numerators are 1205,1199
Denominators are 300,565
The GCF of 1205,1199 is 1 .
LCM of 300,565 is 33900.
The greatest common factor of 1205/300,1199/565 = [GCF of 1205,1199]/[LCM of 300,565]= 1/33900
Therefore, the GCF of 1205/300,1199/565 is 1/33900.
To find the highest common factor of 1205,1199, we have to find the factors of both numbers and list the highest common factor.
The factors of 1205 are 1, 5, 241, 1205
The factors of 1199 are 1, 11, 109, 1199
The HCF of 1205,1199 is 1.
Lets's calculate GCF of 1205,1199
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1205,1199 By Matching Biggest Common Factor Method
Now, list down the factors of 1205
:1,5,241,1205
Now, list down the factors of 1199
:1,11,109,1199
Greatest Common Factor
We found the factors 1205,1199 . The biggest common factor number is the GCF number.
So the greatest common factor 1205,1199 is 1.
Lets's calculate LCM of 300,565
| 5 | 300, 565 |
| 60, 113 |
∴ So the LCM of the given numbers is 5 x 60 x 113 = 33900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33900
Therefore, the GCF of Fractions 1205/300,1199/565 is 1/33900
Least Common Multiple of 300,565 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 300,565 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(300,565) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(300,565) x common factors =5 x 1 = 5
LCM(300,565) = ( 300 × 565 ) / 5
LCM(300,565) = 169500 / 5
LCM(300,565) = 33900
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FAQs on GCF of Fractions of 1205/300, 1199/565
1. What is the HCF of 1205,1199?
The HCF of 1205,1199 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 1205/300, 1199/565?
Answer: GCF of Numerators as per given numbers 1205/300, 1199/565 is
GCF of Numerators i.e. for 1205,1199 is 1
LCM of denominators i.e. for 300,565 is 33900.
Thus, GCF of Fractions is 1/33900.Finally, GCF of Fractions for 1205/300, 1199/565 is 1/33900.