GCF of 365/34, 334/310
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 365/34, 334/310 i.e 1/5270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 365/34, 334/310.
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 365/34,334/310?
Given fractions are 365/34,334/310
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 365/34,334/310, numerators are 365,334
Denominators are 34,310
The GCF of 365,334 is 1 .
LCM of 34,310 is 5270.
The greatest common factor of 365/34,334/310 = [GCF of 365,334]/[LCM of 34,310]= 1/5270
Therefore, the GCF of 365/34,334/310 is 1/5270.
To find the highest common factor of 365,334, we have to find the factors of both numbers and list the highest common factor.
The factors of 365 are 1, 5, 73, 365
The factors of 334 are 1, 2, 167, 334
The HCF of 365,334 is 1.
Lets's calculate GCF of 365,334
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 365,334 By Matching Biggest Common Factor Method
Now, list down the factors of 365
:1,5,73,365
Now, list down the factors of 334
:1,2,167,334
Greatest Common Factor
We found the factors 365,334 . The biggest common factor number is the GCF number.
So the greatest common factor 365,334 is 1.
Lets's calculate LCM of 34,310
| 2 | 34, 310 |
| 17, 155 |
∴ So the LCM of the given numbers is 2 x 17 x 155 = 5270
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5270
Therefore, the GCF of Fractions 365/34,334/310 is 1/5270
Least Common Multiple of 34,310 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 34,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,310) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,310) x common factors =2 x 1 = 2
LCM(34,310) = ( 34 × 310 ) / 2
LCM(34,310) = 10540 / 2
LCM(34,310) = 5270
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FAQs on GCF of Fractions of 365/34, 334/310
1. What is the HCF of 365,334?
The HCF of 365,334 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 365/34, 334/310?
Answer: GCF of Numerators as per given numbers 365/34, 334/310 is
GCF of Numerators i.e. for 365,334 is 1
LCM of denominators i.e. for 34,310 is 5270.
Thus, GCF of Fractions is 1/5270.Finally, GCF of Fractions for 365/34, 334/310 is 1/5270.