GCF of 800/769, 6780/1953
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 800/769, 6780/1953 i.e 20/1501857 easily. The following is the detailed procedure to determine the greatest common factor of fractions 800/769, 6780/1953.
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 800/769,6780/1953?
Given fractions are 800/769,6780/1953
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 800/769,6780/1953, numerators are 800,6780
Denominators are 769,1953
The GCF of 800,6780 is 20 .
LCM of 769,1953 is 1501857.
The greatest common factor of 800/769,6780/1953 = [GCF of 800,6780]/[LCM of 769,1953]= 20/1501857
Therefore, the GCF of 800/769,6780/1953 is 20/1501857.
To find the highest common factor of 800,6780, we have to find the factors of both numbers and list the highest common factor.
The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
The factors of 6780 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 113, 226, 339, 452, 565, 678, 1130, 1356, 1695, 2260, 3390, 6780
The HCF of 800,6780 is 20.
Lets's calculate GCF of 800,6780
| 2 | 800, 6780 |
| 2 | 400, 3390 |
| 5 | 200, 1695 |
| 40, 339 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 800,6780 By Matching Biggest Common Factor Method
Now, list down the factors of 800
:1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800
Now, list down the factors of 6780
:1,2,3,4,5,6,10,12,15,20,30,60,113,226,339,452,565,678,1130,1356,1695,2260,3390,6780
Greatest Common Factor
We found the factors 800,6780 . The biggest common factor number is the GCF number.
So the greatest common factor 800,6780 is 20.
Lets's calculate LCM of 769,1953
Given numbers has no common factors except 1. So, there LCM is their product i.e 1501857
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1501857
Therefore, the GCF of Fractions 800/769,6780/1953 is 20/1501857
Least Common Multiple of 769,1953 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 769,1953 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(769,1953) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(769,1953) x common factors =1 x 1 = 1
LCM(769,1953) = ( 769 × 1953 ) / 1
LCM(769,1953) = 1501857 / 1
LCM(769,1953) = 1501857
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 800/769, 6780/1953
1. What is the HCF of 800,6780?
The HCF of 800,6780 is 20
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 800/769, 6780/1953?
Answer: GCF of Numerators as per given numbers 800/769, 6780/1953 is
GCF of Numerators i.e. for 800,6780 is 20
LCM of denominators i.e. for 769,1953 is 1501857.
Thus, GCF of Fractions is 20/1501857.Finally, GCF of Fractions for 800/769, 6780/1953 is 20/1501857.