a) Find all of the numbers between 1 and 1,000 that have 2 as their only prime factor.

b) What is the next number after 1,000 that had 2 as its only prime fractor?

2 answers

(a) that would be the powers of 2: 1,2,4,...
(b) 1024 = 2^10
a)

The only such numbers are the powers of 2:

2¹ = 2

2² =4

2³ = 8

2⁴ = 16,

2⁵ = 32

2⁶ = 64

2⁷ = 128

2⁸ = 256

and

2⁹ = 512

All other numbers are either non-prime or, if prime, are not divisible by 2.

b)

2¹⁰ =1024

Because all the numbers between 1 and 1000 that have 2 as their only prime