If a number leaves a remainder of 5 when divided by 8, what will be the remainde

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Question: If a number leaves a remainder of 5 when divided by 8, what will be the remainder when this number is divided by 4?

Options:

Correct Answer: 1

Solution:

If the number is 8k + 5, then when divided by 4, the remainder is 1 (5 % 4 = 1).

If a number leaves a remainder of 5 when divided by 8, what will be the remainder when this number is divided by 4?

If a number leaves a remainder of 5 when divided by 8, what will be the remainder when this number is divided by 4?

Step 1: Understand that the number leaves a remainder of 5 when divided by 8. This means the number can be expressed as 8k + 5, where k is any whole number.
Step 2: To find the remainder when this number is divided by 4, we can use the expression 8k + 5.
Step 3: Divide 8k by 4. Since 8 is a multiple of 4, 8k divided by 4 leaves no remainder.
Step 4: Now, focus on the 5 in the expression. We need to find the remainder of 5 when divided by 4.
Step 5: Calculate 5 divided by 4. The quotient is 1 and the remainder is 1 (because 5 = 4 * 1 + 1).
Step 6: Therefore, the remainder when the original number (8k + 5) is divided by 4 is 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Divisibility Rules – Applying rules of divisibility to find remainders.