MGF 1107, SPRING 2016 PRACTICE QUESTIONS FOR EXAM #1

1. Perform the following number base conversions:

(24)10 to base 2

(10010011)2 to base 16

(3A4)16 to base 10

2. Identify each of the following numbers as prime, semi-prime, or composite. (Semi- primes are products of exactly two prime numbers. e.g., 85 = 5 x 17.)

30 445 23 33 101

3. Find the unique prime factorization for each of the following numbers:

57 440 153 242 3025 98

4. Which of the following is true about the number (212 – 1)? (a) it is prime (b) it is composite (c) it is neither prime nor composite (d) it is both prime and composite

5. Euler’s formula fails for n = 41. Why?

6. Verify that Escott’s formula yields a prime number for n = 30.

7. Verify that 28 is a perfect number.

8. Identify each of the following numbers as perfect, deficient, or abundant:

16 38 18

9. Express each of the following as the sum of two prime numbers: 14 10 22 38

10. Find three ways to express 36 as the sum of two prime numbers.

11. One of Fermat’s theorems is that an odd prime number can be expressed as the difference of two perfect squares in one and only one way. Express the number 13 as the difference of two perfect squares.

12. Find the Greatest Common Divisor of the following pairs of numbers:

48 and 80 22, 66, and 242 198 and 1287

13. Find the Least Common Multiple of the following pairs of numbers:

34 and 6 60 and 105 340 and 782

14. Find the fifth Fibonacci number.

15. Find the tenth Fibonacci number.

16. What is the relationship between the Fibonacci sequence and the Golden Ratio?

BONUS QUESTION: A palindrome is a word or number that is the same when the characters are arranged forward or backward. Examples are “radar” and 58085. Which palindromic between 100 and 200 are also prime?