Division Rules in Number Systems

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Questions and Answers

What is the remainder when 45342 is divided by 9?

  • 4
  • 1
  • 0 (correct)
  • 2

Which of the following numbers is completely divisible by 12?

  • 74276
  • 78276 (correct)
  • 78726
  • 78286

What is the remainder when 5224 is divided by 9?

  • 5
  • 4 (correct)
  • 0
  • 3

What is the remainder when 24795 is divided by 9?

<p>0 (A)</p> Signup and view all the answers

Which of the following numbers is completely divisible by 4?

<p>48672 (D)</p> Signup and view all the answers

Which of the following is a property of numbers divisible by 9?

<p>The sum of the digits must be divisible by 9 (C)</p> Signup and view all the answers

The sum of the digits of 78726 is:

<p>30 (A)</p> Signup and view all the answers

Which number will leave a remainder of 4 when divided by 9?

<p>5224 (D)</p> Signup and view all the answers

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Study Notes

Divisibility Rules

  • A number is divisible by 9 if the sum of its digits is divisible by 9.
  • A number is divisible by 4 if its last two digits are divisible by 4.
  • A number is divisible by 3 if the sum of its digits is divisible by 3.

Examples

  • When 45342 is divided by 9, the remainder is 0 because the sum of its digits (4+5+3+4+2 = 18) is divisible by 9.
  • The number 78276 is fully divisible by 12 because it passes the divisibility rules for 4 (last two digits 76 are divisible by 4) and 3 (sum of all digits 7+8+2+7+6 = 30 is divisible by 3).
  • When 5224 is divided by 9, the remainder is 4 because the sum of its digits (5+2+2+4 = 13) leaves a remainder of 4 when divided by 9.
  • When 24795 is divided by 9, the remainder is 0 because the sum of its digits (2+4+7+9+5 = 27) is divisible by 9.

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