What is the smallest 5-digit number and how can it be represented using a prime factor tree diagram?

The smallest 5-digit number is 10000. To express this number using its prime factors, we can break it down systematically.

First, we start by finding the prime factorization of 10000. The process involves continuously dividing the number by the smallest prime numbers until we reach 1.

Here’s how the prime factor tree diagram for 10000 looks:

                10000
               /     \
           100      100
           /  \     /  \
         10    10  10    10
        / \    / \  / \   / \
       5   2  5   2 5   2 5   2

From the diagram, we can see that 10000 can be expressed as:

10000 = 2^4 * 5^4

This means that the prime factors of 10000 are 2 and 5, and their respective powers indicate how many times each factor is multiplied together to form the number.

In conclusion, the smallest 5-digit number, 10000, can be represented in prime factorization as 2 raised to the power of 4 and 5 raised to the power of 4.