Octal Division and Remainder Operations Quiz

To divide 45₈ by 6₈ in octal, first convert both numbers to decimal: 45₈ is 37 in decimal and 6₈ is 6. Dividing 37 by 6 gives 6 with a remainder of 1. Converting the quotient back to octal results in 7₈, which is the final answer.

To find the remainder when 37₈ (which is 3×8 + 7 = 31 in decimal) is divided by 5₈ (which is 5 in decimal), we calculate 31 ÷ 5, which gives a quotient of 6 and a remainder of 1. Converting the remainder back to base 8, we find it is 2₈.

To divide 62₈ by 7₈, first convert both numbers to decimal: 62₈ is 50 in decimal, and 7₈ is 7. Dividing 50 by 7 gives 7 with a remainder of 1. Convert the quotient (7) back to octal, which is 10₈. Thus, the final answer is 10₈.

To find the remainder of 54₈ when divided by 6₈, we first convert both numbers from base 8 to base 10. 54₈ equals 44 in base 10, and 6₈ equals 6. Dividing 44 by 6 gives a quotient of 7 and a remainder of 2, which is incorrect. The correct calculation shows that 54₈ is divisible by 6₈ without remainder, resulting in 0.

To divide 76₈ by 4₈, first convert both numbers to decimal: 76₈ is 62 and 4₈ is 4. Dividing 62 by 4 gives 15.5 in decimal, which converts back to 17 in octal (17₈). Thus, the result of 76₈ ÷ 4₈ is 17₈.

To find the remainder of 51₈ mod 7₈, first convert 51₈ to decimal, which equals 41. Then, convert 7₈ to decimal, which equals 7. Now, calculate 41 mod 7, resulting in a remainder of 2. Thus, 51₈ mod 7₈ equals 2.

To divide 100₈ by 3₈, first convert both numbers to decimal: 100₈ is 64 in decimal, and 3₈ is 3 in decimal. Dividing 64 by 3 gives 21 with a remainder of 1. Converting 21 back to octal results in 27₈, which is the quotient.

To find the remainder of 43₈ divided by 5₈, first convert both numbers to decimal. 43₈ equals 35 in decimal and 5₈ equals 5 in decimal. Dividing 35 by 5 gives a quotient of 7 with a remainder of 0. However, to express the answer in base 8, we find that the remainder in base 8 is 3₈.

To divide 77 in base 8 by 6 in base 8, first convert both numbers to decimal. 77₈ equals 63 in decimal, and 6₈ equals 6. Dividing 63 by 6 gives 10.5 in decimal, which is 12 in base 8. Thus, the quotient in base 8 is 12.

To find the remainder when 65₈ (octal) is divided by 4₈, first convert both numbers to decimal. 65₈ equals 53 in decimal, and 4₈ equals 4. Dividing 53 by 4 gives a quotient of 13 and a remainder of 1. Thus, the remainder of 65₈ divided by 4₈ is 1.

To divide 123₈ by 5₈, first convert both numbers to decimal. 123₈ equals 83 in decimal and 5₈ equals 5 in decimal. Dividing 83 by 5 gives 16.6 in decimal, which is 20 in octal. The remainder is 3, which, when added to the quotient, gives 23₈. Thus, the final answer is 23₈.

In base 8, dividing 47₈ (which is 39 in decimal) by 3₈ (which is 3 in decimal) gives a quotient of 15₈ (which is 13 in decimal) with a remainder of 2₈ (which is 2 in decimal). Thus, the statement is true as the division aligns with base 8 arithmetic.