If a number is congruent to 0 modulo 6, which of the following could be a possib

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Question: If a number is congruent to 0 modulo 6, which of the following could be a possible value?

Options:

Correct Answer: 12

Solution:

A number congruent to 0 mod 6 must be a multiple of 6. 12 is a multiple of 6.

If a number is congruent to 0 modulo 6, which of the following could be a possible value?

If a number is congruent to 0 modulo 6, which of the following could be a possible value?

Step 1: Understand what 'congruent to 0 modulo 6' means. It means that when you divide the number by 6, there is no remainder.
Step 2: Identify what it means to be a multiple of 6. A multiple of 6 is any number that can be expressed as 6 times an integer (like 6, 12, 18, etc.).
Step 3: Check if the number 12 is a multiple of 6. Since 12 divided by 6 equals 2 with no remainder, 12 is indeed a multiple of 6.
Step 4: Conclude that since 12 is a multiple of 6, it is a possible value for a number that is congruent to 0 modulo 6.

Modular Arithmetic – Understanding congruence relations and their implications for divisibility.
Multiples – Recognizing that a number congruent to 0 modulo n is a multiple of n.