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# Meet Mike Zabrocki

Dr. Zabrocki is looking forward to joining your class. You can use the information below to prepare for our visit.

#### Teacher Resources

Dr. Zabrocki will be speaking about Cryptocurrencies in his talk.

Below are a few concepts you should review with your students prior to the talk if possible.

There are also a few videos you can show your students as well!

#### Factors

These are the whole numbers that evenly divide a number. For example:

• the factors of 8 are 2 and 4
• the factors of 12 are 2, 3, 4 and 6
• the factors of 25 (a square number) is 5
• 13 has no factors, so it is a prime number

#### Prime Factorization

This is the unique set of prime numbers that make up any other number. For example, the prime factorization of 8 is 2 x 2 x 2.

A prime factorization is made up of only prime numbers, multiplied together. The factors of 18 are 2, 3, 6, and 9. However, the prime factorization of 18 is 2 x 3 x 3 (as we are only using prime numbers, of which 6 and 9 are not).

Every number can be written as a unique combination of prime factors. You can explore these more here as well: https://mathigon.org/polypad (under Prime Factor Circles and Dot Arrangements)

The reason 1 is excluded as a prime number (and therefore in the prime factorizations) is because, if we include it, we can no longer write numbers as UNIQUE products of primes.

For example we could write 8 = 2 x 2 x 2 OR 8 = 2 x 2 x 2 x 1 OR 8 = 2 x 2 x 2 x 1 x 1

Since multiplying by 1 doesn’t change the number we could add as many 1’s as we wanted, so there would no longer be a single unique representation of each number.

So we write our definition of a prime number to exclude 1 from being prime in the first place so we don’t have this issue.