Math Activity: Intro To Projects And Primes Page 4

The last part of our look into primes considers division of two numbers as a process of comparing

primes.

6. Answer the following with your group:

a) Is 24 divisible by 2?

b) Does 24 have a 2 in its prime factorization?

c) Is 56 divisible by 14?

d) Does the prime factorization of 56 contain all the primes from 14’s prime factorization?

e) Is 630 divisible by 126?

f) Does the prime factorization of 630 contain all the primes from 126’s prime factorization?

g) Is 88 divisible by 33?

h) Can you generalize why 88 is not divisible by 33 using the idea of prime numbers?

The examples above demonstrate that the only way a number can be divided evenly is if the dividend

(the first number) has all the primes in its prime factorization found in the prime factorization of the

divisor (the second number).

Here is a visual demonstration from 6 e).

Here is a visual demonstration from 6 g).

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