Prime Numbers

Question 1

Prime number = integer greater than 1 with no factors except for 1 and itself

Prime factor vs unique prime factor

Answer 1

Prime numbers:
2, 3, 5, 7, 
11, 13, 17, 19, 
23, 29, 
31, 37
41, 43, 47
53, 59 
61, 67
71, 73, 79, 
83, 89
97 

2 is only even prime number and also smallest prime number.

Question 2

Composite numbers

Number that is not prime

Answer 2

Can do prime factorization to It

Use divisibilité tricks to see what divides into it

Question 3

If you know that x and y are not equal. And you are asked if y is divisible by x

If you’re told x and y have the same no of prime factors, but you know they are not the same

Then y is not divisible by x

Answer 3

Eg
X= 4 and y= 9: x has two 2s and Y has two 3s. But y not divisible by x

X = 12 and y = 18: x has two 2s and one 3; y ha two 3s and one 2. But y not divisible by x

Let’s assume x and y both have k prime factors.
PF x = p1 x p2 x p3
PF y = Q1 x q2 x q3

Assume y/x

P1 would have to equal Q1 etc
But told x cannot equal y