Use our free GCF of Fractions Calculator tool to compute the GCF of 412/862, 456/464 i.e 4/199984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/862, 456/464.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 412/862,456/464
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 412/862,456/464, numerators are 412,456
Denominators are 862,464
The GCF of 412,456 is 4 .
LCM of 862,464 is 199984.
The greatest common factor of 412/862,456/464 = [GCF of 412,456]/[LCM of 862,464]= 4/199984
Therefore, the GCF of 412/862,456/464 is 4/199984.
To find the highest common factor of 412,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 412,456 is 4.
Lets's calculate GCF of 412,456
2 | 412, 456 |
2 | 206, 228 |
103, 114 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 412,456 . The biggest common factor number is the GCF number.
So the greatest common factor 412,456 is 4.
Lets's calculate LCM of 862,464
2 | 862, 464 |
431, 232 |
∴ So the LCM of the given numbers is 2 x 431 x 232 = 199984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/199984
Therefore, the GCF of Fractions 412/862,456/464 is 4/199984
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 862,464 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(862,464) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(862,464) x common factors =2 x 1 = 2
LCM(862,464) = ( 862 × 464 ) / 2
LCM(862,464) = 399968 / 2
LCM(862,464) = 199984
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 412,456?
The HCF of 412,456 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 412/862, 456/464?
Answer: GCF of Numerators as per given numbers 412/862, 456/464 is
GCF of Numerators i.e. for 412,456 is 4
LCM of denominators i.e. for 862,464 is 199984.
Thus, GCF of Fractions is 4/199984.Finally, GCF of Fractions for 412/862, 456/464 is 4/199984.