Use our free GCF of Fractions Calculator tool to compute the GCF of 462/529, 928/759 i.e 2/17457 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/529, 928/759.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 462/529,928/759
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 462/529,928/759, numerators are 462,928
Denominators are 529,759
The GCF of 462,928 is 2 .
LCM of 529,759 is 17457.
The greatest common factor of 462/529,928/759 = [GCF of 462,928]/[LCM of 529,759]= 2/17457
Therefore, the GCF of 462/529,928/759 is 2/17457.
To find the highest common factor of 462,928, we have to find the factors of both numbers and list the highest common factor.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 928 are 1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928
The HCF of 462,928 is 2.
Lets's calculate GCF of 462,928
2 | 462, 928 |
231, 464 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 928
:1,2,4,8,16,29,32,58,116,232,464,928
Greatest Common Factor
We found the factors 462,928 . The biggest common factor number is the GCF number.
So the greatest common factor 462,928 is 2.
Lets's calculate LCM of 529,759
23 | 529, 759 |
23, 33 |
∴ So the LCM of the given numbers is 23 x 23 x 33 = 17457
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/17457
Therefore, the GCF of Fractions 462/529,928/759 is 2/17457
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 529,759 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(529,759) = 23
common factors(in case of two or more numbers have common factors) = 1
GCF(529,759) x common factors =23 x 1 = 23
LCM(529,759) = ( 529 × 759 ) / 23
LCM(529,759) = 401511 / 23
LCM(529,759) = 17457
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 462,928?
The HCF of 462,928 is 2
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 462/529, 928/759?
Answer: GCF of Numerators as per given numbers 462/529, 928/759 is
GCF of Numerators i.e. for 462,928 is 2
LCM of denominators i.e. for 529,759 is 17457.
Thus, GCF of Fractions is 2/17457.Finally, GCF of Fractions for 462/529, 928/759 is 2/17457.