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Juan Espino Kolossa MAT 243 ONLINE A Spring 2017 Assignment Unit13 Prime Numbers GCD Euklid Algorithm LCM due 02/05/2017 at 11:59pm MST 1. (1 point) Are the following integers primes? Enter ”1” for a prime and ”0” otherwise. 1. 72 2. 46 3. 23 4. 197 5. 102 6. 144 3 0 2 1 0 0 0 0 4 0 0 0 2. (1 point) Find the prime factorization of the follwing num- 0 3 0 2 1 0 0 0 0 4 0 0 0
bers: (write p 0 if a prime does not appear in the given number.) 300 = 2 a 3 b 5 c 7 d 11 e 13 f 17 g 19 h where a = b = c = d = e = f = g = h = 0 1 1 2 0 3. (1 point) What are the greatest common divisors of the following pairs of integers? (a) 2 2 · 3 3 · 5 3 and 2 4 · 3 5 · 5 41327 = 2 a 3 b 5 c 7 d 11 e 13 f 17 g 19 h where a = b = c = d = e = f = g = h = ( 2 ) 0 1 1 2 0 3. (1 point) What are the greatest common divisors of the following pairs of integers? (a) 2 2 · 3 3 · 5 3 and 2 4 · 3 5 · 5 φ ( 2 )
φ ( 4 ) φ ( 6 ) φ ( 18 )
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6 5. (1 point) Suppose an integer x is divisible by 21. What other positive integers must also divide x ? [Hint: Think about the transitivity of ”divides.” Enter your an- swer as a comma-separated list.] Suppose an integer a is divisible by 16. What other positive integers must also divide a ? [Enter your answer as a comma-separated list.]