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