GCF of 374/143, 509/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 374/143, 509/319 i.e 1/4147 easily. The following is the detailed procedure to determine the greatest common factor of fractions 374/143, 509/319.
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 374/143,509/319?
Given fractions are 374/143,509/319
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 374/143,509/319, numerators are 374,509
Denominators are 143,319
The GCF of 374,509 is 1 .
LCM of 143,319 is 4147.
The greatest common factor of 374/143,509/319 = [GCF of 374,509]/[LCM of 143,319]= 1/4147
Therefore, the GCF of 374/143,509/319 is 1/4147.
To find the highest common factor of 374,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374
The factors of 509 are 1, 509
The HCF of 374,509 is 1.
Lets's calculate GCF of 374,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 374,509 By Matching Biggest Common Factor Method
Now, list down the factors of 374
:1,2,11,17,22,34,187,374
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 374,509 . The biggest common factor number is the GCF number.
So the greatest common factor 374,509 is 1.
Lets's calculate LCM of 143,319
| 11 | 143, 319 |
| 13, 29 |
∴ So the LCM of the given numbers is 11 x 13 x 29 = 4147
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4147
Therefore, the GCF of Fractions 374/143,509/319 is 1/4147
Least Common Multiple of 143,319 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 143,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(143,319) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(143,319) x common factors =11 x 1 = 11
LCM(143,319) = ( 143 × 319 ) / 11
LCM(143,319) = 45617 / 11
LCM(143,319) = 4147
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FAQs on GCF of Fractions of 374/143, 509/319
1. What is the HCF of 374,509?
The HCF of 374,509 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 374/143, 509/319?
Answer: GCF of Numerators as per given numbers 374/143, 509/319 is
GCF of Numerators i.e. for 374,509 is 1
LCM of denominators i.e. for 143,319 is 4147.
Thus, GCF of Fractions is 1/4147.Finally, GCF of Fractions for 374/143, 509/319 is 1/4147.