common factors of 132 and 429
The common factors of 132 and 429 are: 1 and 3.
To find the common factors of 132 and 429, we can start by finding the prime factorizations of both numbers.
Let's start with 132:
Divide 132 by the smallest prime number, which is 2:
132 ÷ 2 = 66
Divide 66 by 2:
66 ÷ 2 = 33
Since 33 is an odd number, we cannot divide it any further by 2. Let's try the next prime number, 3:
33 ÷ 3 = 11
11 is a prime number, so the prime factorization of 132 is 2 × 2 × 3 × 11, which can be written as 2^2 × 3 × 11.
Now let's find the prime factorization of 429:
Divide 429 by 3:
429 ÷ 3 = 143
Divide 143 by 11:
143 ÷ 11 = 13
13 is a prime number, so the prime factorization of 429 is 3 × 11 × 13, which can be written as 3 × 11 × 13.
Now that we have the prime factorizations, we can find the common factors by identifying the common prime factors. In this case, the only common prime factor is 11.
Therefore, the common factors of 132 and 429 are 1, 11.
To find the common factors of 132 and 429, we need to determine the numbers that can divide both of these numbers evenly.
First, let's find the factors of 132:
The factors of 132 are:
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.
Next, let's find the factors of 429:
The factors of 429 are:
1, 3, 11, 13, 33, 39, 143, and 429.
Therefore, the common factors of 132 and 429 are 1 and 3.