1. Does 17 divide each of these numbers?a) 68 b) 84 c) 357 d) 10012. What are the quotient and remainder whena) 19 is divided by 7? b) −111 is divided by 11? c) 789 is divided by 23?d) 1001 is divided by 13? e) 0 is divided by 19? f ) 3 is divided by 5?
Question
- Does 17 divide each of these numbers?a) 68 b) 84 c) 357 d) 10012. What are the quotient and remainder whena) 19 is divided by 7? b) −111 is divided by 11? c) 789 is divided by 23?d) 1001 is divided by 13? e) 0 is divided by 19? f ) 3 is divided by 5?
Solution
a) 68 divided by 17 equals 4, so yes, 17 divides 68. b) 84 divided by 17 equals 4.94, which is not a whole number, so no, 17 does not divide 84. c) 357 divided by 17 equals 21, so yes, 17 divides 357. d) 1001 divided by 17 equals 58.88, which is not a whole number, so no, 17 does not divide 1001.
a) When 19 is divided by 7, the quotient is 2 and the remainder is 5. b) When -111 is divided by 11, the quotient is -10 and the remainder is 0. c) When 789 is divided by 23, the quotient is 34 and the remainder is 3. d) When 1001 is divided by 13, the quotient is 77 and the remainder is 0. e) When 0 is divided by 19, the quotient is 0 and the remainder is 0. f) When 3 is divided by 5, the quotient is 0 and the remainder is 3.
Similar Questions
5. Find a div m and a mod m whena) a = −111, m = 99. b) a = −9999, m = 101.c) a = 10299, m = 999. d) a = 123456, m = 1001.6. Decide whether each of these integers is congruent to 5 modulo 17.a) 80 b) 103 c) −29 d) −1227. Find each of these values.a) (992 mod 32)3 mod 15 b) (34 mod 17)2 mod 11c) (193 mod 23)2 mod 31 d) (893 mod 79)4 mod 268. Convert the decimal expansion of each of these integers to a binary expansion.a) 23 b) 45 c) 241 d) 10259. Convert the binary expansion of each of these integers to a decimal expansion.a) (1 1011)2 b) (10 1011 0101)2c) (11 1011 1110)2 d) (111 1100 0001 1111)2
17. Which of the following numbers give a remainder of 2 when divided by 5 and a remainder of 1 when divided by 4? A. 7 C. 17 B. 12 D. 31
6. Determine the base of the numbers in each case for the following operations to be correct: (a) 14/2 = 5 [0.5 mark] (b) 54/4 = 13 [0.5 mark] (c) 24 + 17 = 40
1. Determine whether each of these integers is prime.a) 21 b) 29 c) 71 d) 97e) 111 f ) 143 g) 93 h) 1012. Find the prime factorization of each of these integers.a) 39 b) 81 c) 101d) 143 e) 289 f ) 899
8. QUESTION7 5 10 7 21 17 ?
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