How do you write the prime factorization of 110?

To find the prime factorization of 110, we need to break it down into its prime factors. Prime factors are the prime numbers that multiply together to give the original number. Let's go through the steps to find the prime factorization of 110.

Step-by-Step Breakdown

First, we start with the number 110. The goal is to divide it by the smallest prime numbers until we can no longer divide evenly.

Identifying the Smallest Prime Factor

The smallest prime number is 2. Since 110 is an even number, we can divide it by 2:

• 110 ÷ 2 = 55

Now we have 2 as one of our prime factors, and we are left with 55.

Factoring 55

Next, we need to factor 55. The smallest prime number we can try is again 2, but since 55 is odd, we move to the next prime number, which is 3. However, 55 is not divisible by 3 either. The next prime number is 5:

• 55 ÷ 5 = 11

Now we have another prime factor, which is 5, and we are left with 11.

Final Prime Factor

At this point, we need to check if 11 is a prime number. A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. Since 11 fits this definition, we conclude that it is prime.

Putting It All Together

Now that we have factored 110 completely, we can express it as a product of its prime factors:

• 110 = 2 × 5 × 11

Thus, the prime factorization of 110 is 2, 5, and 11. This means that if you multiply these prime numbers together, you will get back to 110.

Visualizing the Process

To visualize this, you can think of it like breaking down a complex puzzle into simpler pieces. Each prime factor is like a piece of the puzzle that, when combined, forms the complete picture of the original number.

In summary, the prime factorization of 110 is 2 × 5 × 11, and this method can be applied to any composite number to find its prime factors.