Use our free GCF of Fractions Calculator tool to compute the GCF of 822/768, 499/410 i.e 1/157440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 822/768, 499/410.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 822/768,499/410
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 822/768,499/410, numerators are 822,499
Denominators are 768,410
The GCF of 822,499 is 1 .
LCM of 768,410 is 157440.
The greatest common factor of 822/768,499/410 = [GCF of 822,499]/[LCM of 768,410]= 1/157440
Therefore, the GCF of 822/768,499/410 is 1/157440.
To find the highest common factor of 822,499, we have to find the factors of both numbers and list the highest common factor.
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822
The factors of 499 are 1, 499
The HCF of 822,499 is 1.
Lets's calculate GCF of 822,499
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Now, list down the factors of 499
:1,499
Greatest Common Factor
We found the factors 822,499 . The biggest common factor number is the GCF number.
So the greatest common factor 822,499 is 1.
Lets's calculate LCM of 768,410
2 | 768, 410 |
384, 205 |
∴ So the LCM of the given numbers is 2 x 384 x 205 = 157440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/157440
Therefore, the GCF of Fractions 822/768,499/410 is 1/157440
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 768,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(768,410) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(768,410) x common factors =2 x 1 = 2
LCM(768,410) = ( 768 × 410 ) / 2
LCM(768,410) = 314880 / 2
LCM(768,410) = 157440
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 822,499?
The HCF of 822,499 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 822/768, 499/410?
Answer: GCF of Numerators as per given numbers 822/768, 499/410 is
GCF of Numerators i.e. for 822,499 is 1
LCM of denominators i.e. for 768,410 is 157440.
Thus, GCF of Fractions is 1/157440.Finally, GCF of Fractions for 822/768, 499/410 is 1/157440.