Use our free GCF of Fractions Calculator tool to compute the GCF of 775/218, 782/800 i.e 1/87200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 775/218, 782/800.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 775/218,782/800
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 775/218,782/800, numerators are 775,782
Denominators are 218,800
The GCF of 775,782 is 1 .
LCM of 218,800 is 87200.
The greatest common factor of 775/218,782/800 = [GCF of 775,782]/[LCM of 218,800]= 1/87200
Therefore, the GCF of 775/218,782/800 is 1/87200.
To find the highest common factor of 775,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 775 are 1, 5, 25, 31, 155, 775
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 775,782 is 1.
Lets's calculate GCF of 775,782
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 775
:1,5,25,31,155,775
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 775,782 . The biggest common factor number is the GCF number.
So the greatest common factor 775,782 is 1.
Lets's calculate LCM of 218,800
2 | 218, 800 |
109, 400 |
∴ So the LCM of the given numbers is 2 x 109 x 400 = 87200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/87200
Therefore, the GCF of Fractions 775/218,782/800 is 1/87200
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 218,800 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,800) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,800) x common factors =2 x 1 = 2
LCM(218,800) = ( 218 × 800 ) / 2
LCM(218,800) = 174400 / 2
LCM(218,800) = 87200
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 775,782?
The HCF of 775,782 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 775/218, 782/800?
Answer: GCF of Numerators as per given numbers 775/218, 782/800 is
GCF of Numerators i.e. for 775,782 is 1
LCM of denominators i.e. for 218,800 is 87200.
Thus, GCF of Fractions is 1/87200.Finally, GCF of Fractions for 775/218, 782/800 is 1/87200.