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Chapter 1: Problem 26

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$64$$

Short Answer

Expert verified
64 is a composite number and its prime factorization is \(2^6\).

Step by step solution

01

Identifying Prime or Composite

First identify if the number 64 is prime or composite. Since 64 has more than two distinct divisors (1, 64, 2, 32, 4, 16, 8), it is a composite number
02

Finding Prime Factorization

Next, find its prime factorization. Start by dividing the number by the smallest prime number, which is 2. The result is \( 64 梅 2 = 32 \). Divide the result again by 2 to get \( 32 梅 2 = 16 \). Continue this process until you reach a number that isn't divisible by 2 anymore. Doing this, you get \(16 梅 2 = 8\), \(8 梅 2 = 4\), \(4 梅 2 = 2\), \(2 梅 2 = 1\). So, the prime factorization of 64 is \(2^6\) meaning \(64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2\)
03

Conclusion

Therefore, 64 is a composite number and its prime factorization is \(2^6\)

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Most popular questions from this chapter

Simplify each series of additions and subtractions. $$2-\frac{3}{4}-\left(-\frac{7}{8}\right)$$

A multiplication is expressed as a repeated addition. Find this sum, indicated by a question mark. $$3(-3)=(-3)+(-3)+(-3)=?$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between 6 times a number and \(-5\) times the number.

Find the value of each expression. $$\frac{5}{8}-\left(\frac{1}{2}-\frac{3}{4}\right)$$

The list shows a pattern for various products. $$\begin{aligned}2(-3) &=-6 \\\1(-3) &=-3 \\\0(-3) &=0 \\\\-1(-3) &=3 \\\\-2(-3) &=6 \\\\-3(-3) &=9 \\\\-4(-3) &=? \end{aligned}$$ Use this pattern to find \(-4(-3)\)
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