Why is the prime factorization of 45 equals 3x3x5?

Answer 1

The prime factorization of a number breaks it down into its prime factors. In the case of 45, it can be expressed as 3 x 3 x 5. This is because 45 can be divided by 3 twice and by 5 once, resulting in the prime factors of 3 and 5. This prime factorization represents the unique combination of prime numbers that, when multiplied together, equal 45.

Answer 2

There are two ways to why the prime factorization for 45 equals 3x3x5. First of all, you may start with multiplying it. Start with 3x3; which equals nine or 9. Then 9x5 equals 45. the other way is that you may break it down, starting from 45. first you find 2 factors that you can multiply to receive the answer or product of 45. If you said 9x5 you are correct. So therefore you below the number 45 you may write the equation 9x5. Then you check if any of the numbers can be reduced or simplified. Let's start with the 5: can you find any factors of five? No, so you bring down the 5. How about 9? Yes, 3x3. Are there any others? No, there are no others, unless you include 9x1. But that's too easy. Below the 9 and beside the 5 write the multiplication sign, then 3x3. It should look something like this:

4 5

^

9 x 5

^ ^

3 x 3 x 5

sorry if the computer distorts the prime factorization tree.