GCF of 367/414, 363/464
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 367/414, 363/464 i.e 1/96048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 367/414, 363/464.
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 367/414,363/464?
Given fractions are 367/414,363/464
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 367/414,363/464, numerators are 367,363
Denominators are 414,464
The GCF of 367,363 is 1 .
LCM of 414,464 is 96048.
The greatest common factor of 367/414,363/464 = [GCF of 367,363]/[LCM of 414,464]= 1/96048
Therefore, the GCF of 367/414,363/464 is 1/96048.
To find the highest common factor of 367,363, we have to find the factors of both numbers and list the highest common factor.
The factors of 367 are 1, 367
The factors of 363 are 1, 3, 11, 33, 121, 363
The HCF of 367,363 is 1.
Lets's calculate GCF of 367,363
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 367,363 By Matching Biggest Common Factor Method
Now, list down the factors of 367
:1,367
Now, list down the factors of 363
:1,3,11,33,121,363
Greatest Common Factor
We found the factors 367,363 . The biggest common factor number is the GCF number.
So the greatest common factor 367,363 is 1.
Lets's calculate LCM of 414,464
| 2 | 414, 464 |
| 207, 232 |
∴ So the LCM of the given numbers is 2 x 207 x 232 = 96048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/96048
Therefore, the GCF of Fractions 367/414,363/464 is 1/96048
Least Common Multiple of 414,464 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 414,464 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,464) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,464) x common factors =2 x 1 = 2
LCM(414,464) = ( 414 × 464 ) / 2
LCM(414,464) = 192096 / 2
LCM(414,464) = 96048
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FAQs on GCF of Fractions of 367/414, 363/464
1. What is the HCF of 367,363?
The HCF of 367,363 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 367/414, 363/464?
Answer: GCF of Numerators as per given numbers 367/414, 363/464 is
GCF of Numerators i.e. for 367,363 is 1
LCM of denominators i.e. for 414,464 is 96048.
Thus, GCF of Fractions is 1/96048.Finally, GCF of Fractions for 367/414, 363/464 is 1/96048.