 # Prime Numbers, Numeration Bases & Euclidean Algorithm

Subject Computer Science Discrete Math

## Question

1. Determine whether or not each of the following integers is a prime
a) 9833
b) 150

2. Find q and r as defined by the division algorithm
a) a = -5286; b = 19
b) a = 5286; b = -19

3. Find the binary, octal and hexadecimal representations for each of the following
integers (given in base 10).
a) 57,483
b) 185,178

4. In each of the following cases, find the greatest common divisor (gcd) of a and b
applying the Euclidean algorithm.
a) a = 1575, b = 231
b) a = -3719, b = 8416
c) a = 28,844, b = -15,712

## Solution Preview

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a). Because the number is not very small, we can’t figure by eye if it has a prime divisor or not. This is why we must try all possibilities in order to can decide if it is a prime number or not. This assumes to compute √9833=99.16… and to try dividing 9833 by all prime numbers which are smaller than 99. If none of these divisions give us the remainder 0, it means that 9833 is prime.
9,833 is an odd number, thus it can’t be divided by 2....

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