GCF of 856/405, 1380/514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 856/405, 1380/514 i.e 4/208170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 856/405, 1380/514.
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 856/405,1380/514?
Given fractions are 856/405,1380/514
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 856/405,1380/514, numerators are 856,1380
Denominators are 405,514
The GCF of 856,1380 is 4 .
LCM of 405,514 is 208170.
The greatest common factor of 856/405,1380/514 = [GCF of 856,1380]/[LCM of 405,514]= 4/208170
Therefore, the GCF of 856/405,1380/514 is 4/208170.
To find the highest common factor of 856,1380, we have to find the factors of both numbers and list the highest common factor.
The factors of 856 are 1, 2, 4, 8, 107, 214, 428, 856
The factors of 1380 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690, 1380
The HCF of 856,1380 is 4.
Lets's calculate GCF of 856,1380
| 2 | 856, 1380 |
| 2 | 428, 690 |
| 214, 345 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 856,1380 By Matching Biggest Common Factor Method
Now, list down the factors of 856
:1,2,4,8,107,214,428,856
Now, list down the factors of 1380
:1,2,3,4,5,6,10,12,15,20,23,30,46,60,69,92,115,138,230,276,345,460,690,1380
Greatest Common Factor
We found the factors 856,1380 . The biggest common factor number is the GCF number.
So the greatest common factor 856,1380 is 4.
Lets's calculate LCM of 405,514
Given numbers has no common factors except 1. So, there LCM is their product i.e 208170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/208170
Therefore, the GCF of Fractions 856/405,1380/514 is 4/208170
Least Common Multiple of 405,514 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 405,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,514) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(405,514) x common factors =1 x 1 = 1
LCM(405,514) = ( 405 × 514 ) / 1
LCM(405,514) = 208170 / 1
LCM(405,514) = 208170
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 856/405, 1380/514
1. What is the HCF of 856,1380?
The HCF of 856,1380 is 4
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 856/405, 1380/514?
Answer: GCF of Numerators as per given numbers 856/405, 1380/514 is
GCF of Numerators i.e. for 856,1380 is 4
LCM of denominators i.e. for 405,514 is 208170.
Thus, GCF of Fractions is 4/208170.Finally, GCF of Fractions for 856/405, 1380/514 is 4/208170.