Write 132 as a product of its prime factors

Write 132 as a product of its prime factors

The Correct Answer and Explanation is:

To write 132 as a product of its prime factors, we need to break it down step by step. Here’s how to do it:

Step 1: Divide by the smallest prime number, 2.

132 is an even number, so it’s divisible by 2.

132 ÷ 2 = 66

Now, we have 66.

Step 2: Divide 66 by 2.

66 is also divisible by 2 (because it’s even).

66 ÷ 2 = 33

Now, we have 33.

Step 3: Divide by the next smallest prime number, 3.

33 is divisible by 3 because the sum of its digits (3 + 3 = 6) is divisible by 3.

33 ÷ 3 = 11

Now, we have 11.

Step 4: Check if 11 is prime.

11 is a prime number, meaning it cannot be divided further by any number other than 1 and itself.

So, we have reached the end of our factorization.

Final Answer:

132 = 2 × 2 × 3 × 11

Explanation:

This process is called prime factorization. A prime number is a number greater than 1 that has no divisors other than 1 and itself. In this case, the prime factorization of 132 involves the prime numbers 2, 3, and 11.

• The first division step gave us 2, which is a prime number.
• We continued dividing by 2 until we got 33, which is no longer divisible by 2 but is divisible by 3.
• Finally, 33 divided by 3 gives 11, which is prime, ending the factorization process.

Thus, 132 is written as the product of its prime factors: 2 × 2 × 3 × 11.