Let K be your birth year and let N be your 7-digit phone number. Use Euclid’s Algorithm to find GCD(N, K), GCD(N, K + 1), and GCD(N, K + 2). Use Euclid’s Algorithm to find GCD(N + 1, N) for any...

Let K be your birth year and let N be your 7-digit phone number. Use Euclid’s Algorithm to find GCD(N, K), GCD(N, K + 1), and GCD(N, K + 2).

Use Euclid’s Algorithm to find GCD(N + 1, N) for any positive integer N. Does this show that N and

N þ 1 never have a prime factor in common?

Use Euclid’s Algorithm to find GCD(2N+1, 3N+1) for any positive integer N.

Use “long division” to show that

Convert the following numbers from base 2 to base 10:

(a) 1101{2}

(b) 10 0110{2}

(c) 1111 1111{2}