If a number is divided by 8 and leaves a remainder of 5, what will be the remain

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Question: If a number is divided by 8 and leaves a remainder of 5, what will be the remainder when this number is divided by 4? (2023)

Options:

Correct Answer: 3

Exam Year: 2023

Solution:

The number can be expressed as 8k + 5. When divided by 4, the remainder is 5 mod 4 = 1.

If a number is divided by 8 and leaves a remainder of 5, what will be the remainder when this number is divided by 4? (2023)

If a number is divided by 8 and leaves a remainder of 5, what will be the remainder when this number is divided by 4? (2023)

Step 1: Understand that when a number is divided by 8 and leaves a remainder of 5, it can be written in the form of 8k + 5, where k is any whole number.
Step 2: Now, we need to find the remainder when this number (8k + 5) is divided by 4.
Step 3: Break down the expression 8k + 5. Notice that 8k is divisible by 4 because 8 is a multiple of 4.
Step 4: Since 8k is divisible by 4, it leaves a remainder of 0 when divided by 4.
Step 5: Now, consider the 5 in the expression. We need to find the remainder of 5 when divided by 4.
Step 6: When you divide 5 by 4, it goes 1 time (which is 4) and leaves a remainder of 1.
Step 7: Therefore, the remainder when the original number (8k + 5) is divided by 4 is the same as the remainder of 5 divided by 4, which is 1.

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