Use our free GCF of Fractions Calculator tool to compute the GCF of 299/855, 429/675 i.e 13/12825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 299/855, 429/675.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 299/855,429/675
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 299/855,429/675, numerators are 299,429
Denominators are 855,675
The GCF of 299,429 is 13 .
LCM of 855,675 is 12825.
The greatest common factor of 299/855,429/675 = [GCF of 299,429]/[LCM of 855,675]= 13/12825
Therefore, the GCF of 299/855,429/675 is 13/12825.
To find the highest common factor of 299,429, we have to find the factors of both numbers and list the highest common factor.
The factors of 299 are 1, 13, 23, 299
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The HCF of 299,429 is 13.
Lets's calculate GCF of 299,429
13 | 299, 429 |
23, 33 |
∴ So the GCF of the given numbers is 13 = 13
Now, list down the factors of 299
:1,13,23,299
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Greatest Common Factor
We found the factors 299,429 . The biggest common factor number is the GCF number.
So the greatest common factor 299,429 is 13.
Lets's calculate LCM of 855,675
3 | 855, 675 |
3 | 285, 225 |
5 | 95, 75 |
19, 15 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 19 x 15 = 12825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/12825
Therefore, the GCF of Fractions 299/855,429/675 is 13/12825
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 855,675 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(855,675) = 45
common factors(in case of two or more numbers have common factors) = 1
GCF(855,675) x common factors =45 x 1 = 45
LCM(855,675) = ( 855 × 675 ) / 45
LCM(855,675) = 577125 / 45
LCM(855,675) = 12825
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 299,429?
The HCF of 299,429 is 13
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 299/855, 429/675?
Answer: GCF of Numerators as per given numbers 299/855, 429/675 is
GCF of Numerators i.e. for 299,429 is 13
LCM of denominators i.e. for 855,675 is 12825.
Thus, GCF of Fractions is 13/12825.Finally, GCF of Fractions for 299/855, 429/675 is 13/12825.