Question 5.1.3: Prime Factorization by Division Write 1500 as a product of p......
Prime Factorization by Division
Write 1500 as a product of prime numbers.
Step-by-Step
Because 1500 is an even number, the smallest prime number that divides it is 2. Divide 1500 by 2. Place the quotient, 750, below the 1500. Continue to divide each quotient by the smallest prime number that divides it.
\begin{matrix}2&\fbox{1500}\\2&\fbox{750}\\3&\fbox{375}\\5&\fbox{125}\\5&\fbox{25}\\\downarrow &\underset{\rightarrow }{5}\end{matrix}The final quotient, 5, is a prime number, so we stop. The prime factorization is determined by multiplying all divisors on the left side and the final prime number quotient as shown by the shaded arrow. Thus, the prime factorization of 1500 is
2 · 2 · 3 · 5 · 5 · 5 = 2² · 3 · 5³.
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