(5)6113"? DIVE" 11.3? MUD5-___ e.-3'.I" DIV5= vii-37 MODS— e. is the eel of'imegere {4, T, 15. 1e} pairwise reietiveiy prime? {4) T. Suppose the]. the LCM of two integers is on end their GED is 2. 11' one of the integers is 3!], what is the value of the other integer'? {12} 3. Let x be the deeimel number 455. e. Converter to base 2. b. Convert x to base 3. e. Convert x to base 145. :1. Convert x to base I5.

a. 37 DIV 5 = 7

b. 37 MOD 5 = 2

c. -37 DIV 5 = -8

d. -37 MOD 5 = 3

e. No, the set is not pairwise relatively prime.

7. The other number is 4

8. a. 455₁₀ = 111000111₂

b_. 455₁₀ = 707₈

c. 455₁₀ =  1C7₁₆

d.  455₁₀ =  2035₆

Step-by-step explanation

DIV gives the quotient while MOD gives the remainder of the division problem.

Thus,

a. 37 DIV 5 = 7   and, 

b. 37 MOD 5 = 2

that is,

 37/5 = 7 

remainder = 37- 35 = 2

 

c. -37 DIV 5 = -8  and,

d. -37 MOD 5 = 3

that is,

-37 / 5 = -7.4 or -8

remainder = -37-(-40) = +3

Take note that the remainder cannot be negative.

 

e. If the GCD = 1, the numbers are said to be relatively prime. 

pairwise,

4 and 7 = GCD = 1

4 and 15= GCD= 1

4 and 16 = GCD = 4, not 1, so this is not pairwise relatively prime

7 and 15 = GCD = 1

7 and 16 = GCD = 1

15 and 16 = GCD = 1

Therefore the set is not relatively prime.

 

4(7). given:

 LCM = 60 

GCD = 2

if a = 30 what is b?

LCM method to obtain the greatest common divisor is given as,

GCD (a, b) = (a × b)/ LCM (a, b),

thus,

2= 30b /60

2=0.5b

solving b

b= 2/0.5

b= 4

 

Conversion 

convert 455 to base 2

When we convert decimal to any base, we divide the decimal by the base until the quotient equals 0 and calculate the remainder. The remainders become the destination base digits.

Let us apply, decimal to base 10 we divide by 2
thus,

455 / 2 = 227 remainder 1

227 / 2 = 113 r 1

113 / 2 = 56 r 1

56 / 2 = 28 r 0

28/ 2 = 14 r 0

14/2 = 7 r 0

7/2 = 3 r 1

3/2 = 1 r 1

1/ 2 = 0 r 1  

we stop then read the reaminders upwards,

that is, 111000111₂

Therfore, 455₁₀ = 111000111₂

 

convert 455 to base 8

455/8 = 56 remainder 7

56/8 = 7 remainder 0

7/8 = = 0 remainder 7

since the whole number is already 0, we stop dividing and read the remainders upwards.

That is, 707₈

Therefore, 455₁₀ = 707₈

convert 455 to base 16

455/16 = 28 remainder 7

28/16 = 1 remainder 12 

1/ 16=  0 remainder 1

since the whole number is already 0, we stop dividing and read the remainders upwards.

That is, 1C7₁₆

Therefore, 455₁₀ =  1C7₁₆

recall:

10= A in Hexa

11=B

12= C

13=D

14=E

15=F

 

convert 455 to base 6

455 /6 = 75 r 5

75/6 = 12 r 3

12/6 = 2 r 0

2/6 = 0 r 2

since the whole number is already 0, we stop dividing and read the remainders upwards.

That is, 2035₆

Therefore, 455₁₀ =  2035₆