Find the prime factors of 363 and write the prime factorization, use exponents where possible. Make sure to show and/or explain all your work. (2 points)
To find the prime factors of 363, we start by dividing it by the smallest prime number, which is 2.
363 ÷ 2 = 181 remainder 1
Since 181 is a prime number, the prime factorization of 363 is 2 × 181.
To find the prime factors of 363, we start by dividing it by the smallest prime number, which is 2. However, 363 is not divisible by 2 as it is an odd number.
Next, we try dividing by the next prime number, which is 3.
Since 363 can be divided by 3 evenly, we have:
363 ÷ 3 = 121
Now, we continue the process with the quotient we obtained, which is 121.
Again, dividing 121 by 3:
121 ÷ 3 = 40 with a remainder of 1
Since 121 is not divisible by 3, we move on to the next prime number, which is 5.
Dividing 121 by 5:
121 ÷ 5 = 24 with a remainder of 1
Continuing the process with 24:
24 ÷ 5 = 4 with no remainder
We have now obtained a quotient of 4.
As we continue dividing, we find that 4 can be divided by 2:
4 ÷ 2 = 2
We have reached a quotient of 2, which is a prime number.
So, the prime factorization of 363 is:
363 = 3 × 3 × 5 × 11
Using exponents, we can also write it as:
363 = 3² × 5 × 11