In constructing the Sieve of Eratosthenes for 2 through 100, it was said that any composite in that range had to be a multiple of some prime less than or equal to 7 (since the next prime, 11, is greater than the square root of 100). Explain. Since the next prime after 7 is 11, the smallest composite number whose prime factors are all greater than 7, is Since this is than 100, there are no numbers, from 2 to 100, whose prime composite number from 2 to 100 must be a multiple of some factors are all greater than 7. Therefore, prime number less than or equal to 7.

In constructing the Sieve of Eratosthenes for 2 through 100, it was said that any composite in that range had to be a multiple of some prime less than or equal to 7 (since the next prime, 11, is greater than the square root of 100). Explain. Since the next prime after 7 is 11, the smallest composite number whose prime factors are all greater than 7, is Since this is than 100, there are no numbers, from 2 to 100, whose prime composite number from 2 to 100 must be a multiple of some factors are all greater than 7. Therefore, prime number less than or equal to 7.