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Chapter 5: Problem 26

Find the prime factorization of each composite number. 45

Short Answer

Expert verified
The prime factorization of 45 is \(3^2 \times 5\).

Step by step solution

01

Identify the Lowest Prime Number

The first step is to identify the lowest prime number that divides the composite number without leaving a remainder. In this case, 45 can be divided by the lowest prime number, which is 2, but it leaves a remainder. Thus, the next lowest prime number is considered, which is 3. 45 divided by 3 equals 15.
02

Break Down the Quotient

The quotient obtained from the previous step, which is 15, is then broken down. 15 can be divided by 3, the lowest prime number greater than 2, with no remainder. The quotient is 5.
03

Final Prime Factor Identification

5 is a prime number, as it can only be divided by 1 and itself with no remainder. Therefore, the prime factorization of 45 is \(3 \times 3 \times 5\), or \(3^2 \times 5\) in exponential form.

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Most popular questions from this chapter

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{5}\), when \(a_{1}=4, r=3\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A sequence that is not arithmetic must be geometric.

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(2,6,10,14, \ldots\)

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=5000, r=1\)
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