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In a modular system, if 12 is congruent to 0 modulo n, which of the following mu

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Question: In a modular system, if 12 is congruent to 0 modulo n, which of the following must be true?

Options:

  1. n is a factor of 12
  2. n is greater than 12
  3. n is less than 12
  4. n is a prime number

Correct Answer: n is a factor of 12

Solution: 

For 12 to be congruent to 0 modulo n, n must be a divisor of 12.

In a modular system, if 12 is congruent to 0 modulo n, which of the following mu

Practice Questions

Q1
In a modular system, if 12 is congruent to 0 modulo n, which of the following must be true?
  1. n is a factor of 12
  2. n is greater than 12
  3. n is less than 12
  4. n is a prime number

Questions & Step-by-Step Solutions

In a modular system, if 12 is congruent to 0 modulo n, which of the following must be true?
  • Step 1: Understand what 'congruent to 0 modulo n' means. It means that when you divide 12 by n, there is no remainder.
  • Step 2: This can be written mathematically as 12 % n = 0, where % is the modulo operation.
  • Step 3: If 12 % n = 0, it means that n divides 12 evenly.
  • Step 4: Therefore, n must be a divisor of 12, meaning n can be any number that can multiply with another whole number to give 12.
  • Modular Arithmetic – Understanding congruences and their implications in terms of divisibility.
  • Divisibility – Recognizing that if a number is congruent to 0 modulo n, then n must divide that number.
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