GCF of 449/314, 765/269
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 449/314, 765/269 i.e 1/84466 easily. The following is the detailed procedure to determine the greatest common factor of fractions 449/314, 765/269.
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 449/314,765/269?
Given fractions are 449/314,765/269
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 449/314,765/269, numerators are 449,765
Denominators are 314,269
The GCF of 449,765 is 1 .
LCM of 314,269 is 84466.
The greatest common factor of 449/314,765/269 = [GCF of 449,765]/[LCM of 314,269]= 1/84466
Therefore, the GCF of 449/314,765/269 is 1/84466.
To find the highest common factor of 449,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 449 are 1, 449
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 449,765 is 1.
Lets's calculate GCF of 449,765
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 449,765 By Matching Biggest Common Factor Method
Now, list down the factors of 449
:1,449
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 449,765 . The biggest common factor number is the GCF number.
So the greatest common factor 449,765 is 1.
Lets's calculate LCM of 314,269
Given numbers has no common factors except 1. So, there LCM is their product i.e 84466
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/84466
Therefore, the GCF of Fractions 449/314,765/269 is 1/84466
Least Common Multiple of 314,269 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 314,269 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,269) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(314,269) x common factors =1 x 1 = 1
LCM(314,269) = ( 314 × 269 ) / 1
LCM(314,269) = 84466 / 1
LCM(314,269) = 84466
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FAQs on GCF of Fractions of 449/314, 765/269
1. What is the HCF of 449,765?
The HCF of 449,765 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 449/314, 765/269?
Answer: GCF of Numerators as per given numbers 449/314, 765/269 is
GCF of Numerators i.e. for 449,765 is 1
LCM of denominators i.e. for 314,269 is 84466.
Thus, GCF of Fractions is 1/84466.Finally, GCF of Fractions for 449/314, 765/269 is 1/84466.