1. Find the prime factorization of each ofthese integers: (a) 48 (b) 101 5. Whic

Question

1. Find the prime factorization of each ofthese integers:

(a) 48

(b) 101

5. Which positive integers less than 12 are relativelyprime to 12?

6. Find the greatest commondivisor (GCD) of each of the following pairs ofintegers?

(a) 14,56

(b) 198,132

7. Find the least common multiple (LCM) ofeach of the following pairs of integers:

(a) 7, 8

8. Convert these integers from decimalnotation to binary notation:

(a) 321

9. Convert these integersfrom binary notation to decimalnotation:

(a) 11011

10. Convert these integersfrom hexadecimal notation to binarynotation:

(a)2C

11. What is printed after thefollowing Java statements execute?

int x = 5;

if ((1+5 == 5)||(2+3 <5))

x = 4;

System.out.println(x);

Explanation / Answer

1. Find the prime factorization of each of theseintegers:

(a) 48      3*2*2*2*2

(b) 101     prime number   1*101

5. Which positive integers less than 12 arerelatively prime to 12?      5,7,11

6. Find the greatest common divisor (GCD) ofeach of the following pairs ofintegers?

(a) 14, 56      14

(b) 198, 132    66

7. Find the least common multiple (LCM) of eachof the following pairs of integers:

(a) 7,8         56

8. Convert these integers from decimal notationto binary notation:

(a)321         101000001             (256+64+1)

9. Convert these integers from binary notationto decimal notation:

(a) 11011            16+8+2+1=27

10. Convert these integers from hexadecimalnotation to binary notation:

(a) 2C       101100

11. What is printed after the following Javastatements execute?

int x = 5;

if ((1+5 == 5)||(2+3 <5))

x = 4;

System.out.println(x);   5

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