GCF of 782/57, 379/46, 205/11
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 782/57, 379/46, 205/11 i.e 1/28842 easily. The following is the detailed procedure to determine the greatest common factor of fractions 782/57, 379/46, 205/11.
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 782/57,379/46,205/11?
Given fractions are 782/57,379/46,205/11
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 782/57,379/46,205/11, numerators are 782,379,205
Denominators are 57,46,11
The GCF of 782,379,205 is 1 .
LCM of 57,46,11 is 28842.
The greatest common factor of 782/57,379/46,205/11 = [GCF of 782,379,205]/[LCM of 57,46,11]= 1/28842
Therefore, the GCF of 782/57,379/46,205/11 is 1/28842.
To find the highest common factor of 782,379,205, we have to find the factors of both numbers and list the highest common factor.
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The factors of 379 are 1, 379
The factors of 205 are 1, 5, 41, 205
The HCF of 782,379,205 is 1.
Lets's calculate GCF of 782,379,205
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 782,379,205 By Matching Biggest Common Factor Method
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Now, list down the factors of 379
:1,379
Now, list down the factors of 205
:1,5,41,205
Greatest Common Factor
We found the factors 782,379,205 . The biggest common factor number is the GCF number.
So the greatest common factor 782,379,205 is 1.
Lets's calculate LCM of 57,46,11
Given numbers has no common factors except 1. So, there LCM is their product i.e 28842
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28842
Therefore, the GCF of Fractions 782/57,379/46,205/11 is 1/28842
Least Common Multiple of 57,46,11 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 57,46,11 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,46,11) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(57,46,11) x common factors =1 x 1 = 1
LCM(57,46,11) = ( 57 × 46 × 11 ) / 1
LCM(57,46,11) = 28842 / 1
LCM(57,46,11) = 28842
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 782/57, 379/46, 205/11
1. What is the HCF of 782,379,205?
The HCF of 782,379,205 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 782/57, 379/46, 205/11?
Answer: GCF of Numerators as per given numbers 782/57, 379/46, 205/11 is
GCF of Numerators i.e. for 782,379,205 is 1
LCM of denominators i.e. for 57,46,11 is 28842.
Thus, GCF of Fractions is 1/28842.Finally, GCF of Fractions for 782/57, 379/46, 205/11 is 1/28842.