If a number leaves a remainder of 5 when divided by 12, what will be the remaind

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Question: If a number leaves a remainder of 5 when divided by 12, what will be the remainder when the same number is divided by 4?

Options:

Correct Answer: 2

Solution:

The number can be expressed as 12k + 5. When divided by 4, the remainder is 5 mod 4, which is 1.

If a number leaves a remainder of 5 when divided by 12, what will be the remainder when the same number is divided by 4?

If a number leaves a remainder of 5 when divided by 12, what will be the remainder when the same number is divided by 4?

Step 1: Understand that if a number leaves a remainder of 5 when divided by 12, it can be written in the form of 12k + 5, where k is any whole number.
Step 2: Now, we need to find the remainder of this number (12k + 5) when it is divided by 4.
Step 3: Break down the expression 12k + 5 into two parts: 12k and 5.
Step 4: Calculate the remainder of 12k when divided by 4. Since 12 is a multiple of 4, the remainder is 0.
Step 5: Now, calculate the remainder of 5 when divided by 4. When you divide 5 by 4, the remainder is 1.
Step 6: Combine the results from Step 4 and Step 5. The total remainder when 12k + 5 is divided by 4 is 0 (from 12k) + 1 (from 5) = 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Algebraic Expression – Expressing a number in terms of another variable to analyze its properties.