GCF of 364/208, 5745/145
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 364/208, 5745/145 i.e 1/30160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/208, 5745/145.
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 364/208,5745/145?
Given fractions are 364/208,5745/145
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 364/208,5745/145, numerators are 364,5745
Denominators are 208,145
The GCF of 364,5745 is 1 .
LCM of 208,145 is 30160.
The greatest common factor of 364/208,5745/145 = [GCF of 364,5745]/[LCM of 208,145]= 1/30160
Therefore, the GCF of 364/208,5745/145 is 1/30160.
To find the highest common factor of 364,5745, we have to find the factors of both numbers and list the highest common factor.
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The factors of 5745 are 1, 3, 5, 15, 383, 1149, 1915, 5745
The HCF of 364,5745 is 1.
Lets's calculate GCF of 364,5745
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 364,5745 By Matching Biggest Common Factor Method
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Now, list down the factors of 5745
:1,3,5,15,383,1149,1915,5745
Greatest Common Factor
We found the factors 364,5745 . The biggest common factor number is the GCF number.
So the greatest common factor 364,5745 is 1.
Lets's calculate LCM of 208,145
Given numbers has no common factors except 1. So, there LCM is their product i.e 30160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30160
Therefore, the GCF of Fractions 364/208,5745/145 is 1/30160
Least Common Multiple of 208,145 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 208,145 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,145) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(208,145) x common factors =1 x 1 = 1
LCM(208,145) = ( 208 × 145 ) / 1
LCM(208,145) = 30160 / 1
LCM(208,145) = 30160
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 364/208, 5745/145
1. What is the HCF of 364,5745?
The HCF of 364,5745 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 364/208, 5745/145?
Answer: GCF of Numerators as per given numbers 364/208, 5745/145 is
GCF of Numerators i.e. for 364,5745 is 1
LCM of denominators i.e. for 208,145 is 30160.
Thus, GCF of Fractions is 1/30160.Finally, GCF of Fractions for 364/208, 5745/145 is 1/30160.