When we use the Euclidean algorithm to find gcd(123, 456), what is the quotient in the first division?

Given two positive integers aa and bb with a≥ba \geq b, what is the best asymptotic upper bound of an algorithm that uses prime factorization to find GCD(a, b)?

Given two positive integers aa and bb with a≥ba \geq b, what is the best asymptotic upper bound of the Euclidean algorithm?

Prove that if nnn is even then n2≡0n2≡0n^2 \equiv 0 (mod 44).

Prove that if nn is even then n2≡0n^2 \equiv 0 (mod 44).

Given the following algorithm, matching each statement to the correct sequence for complexity analysis.

procedure bin_exp(b, n): b and n are positive integers

1    x = 1

2    p = b

3    while (n != 0) do

4        if (n mod 2 == 1)

5            x = x * p

6        end of if

7        p = p * p

8        n = n div 2

9    end of while

a    return x

What is the decimal value of an octal number 35103510?

What is the decimal value of a hexadecimal number 744744?

What is the decimal value of an octal number 37443744?

What is the decimal value of a hexadecimal number 77AC?