Use our free GCF of Fractions Calculator tool to compute the GCF of 132/513, 429/156 i.e 33/26676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 132/513, 429/156.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 132/513,429/156
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 132/513,429/156, numerators are 132,429
Denominators are 513,156
The GCF of 132,429 is 33 .
LCM of 513,156 is 26676.
The greatest common factor of 132/513,429/156 = [GCF of 132,429]/[LCM of 513,156]= 33/26676
Therefore, the GCF of 132/513,429/156 is 33/26676.
To find the highest common factor of 132,429, we have to find the factors of both numbers and list the highest common factor.
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The HCF of 132,429 is 33.
Lets's calculate GCF of 132,429
3 | 132, 429 |
11 | 44, 143 |
4, 13 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Greatest Common Factor
We found the factors 132,429 . The biggest common factor number is the GCF number.
So the greatest common factor 132,429 is 33.
Lets's calculate LCM of 513,156
3 | 513, 156 |
171, 52 |
∴ So the LCM of the given numbers is 3 x 171 x 52 = 26676
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/26676
Therefore, the GCF of Fractions 132/513,429/156 is 33/26676
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 513,156 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(513,156) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(513,156) x common factors =3 x 1 = 3
LCM(513,156) = ( 513 × 156 ) / 3
LCM(513,156) = 80028 / 3
LCM(513,156) = 26676
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 132,429?
The HCF of 132,429 is 33
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 132/513, 429/156?
Answer: GCF of Numerators as per given numbers 132/513, 429/156 is
GCF of Numerators i.e. for 132,429 is 33
LCM of denominators i.e. for 513,156 is 26676.
Thus, GCF of Fractions is 33/26676.Finally, GCF of Fractions for 132/513, 429/156 is 33/26676.