If a number is divided by 8 and gives a remainder of 5, what will be the remaind
Practice Questions
Q1
If a number is divided by 8 and gives a remainder of 5, what will be the remainder when this number is divided by 4?
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Questions & Step-by-Step Solutions
If a number is divided by 8 and gives a remainder of 5, what will be the remainder when this number is divided by 4?
Step 1: Understand that when a number is divided by 8 and gives 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 into two parts: 8k and 5.
Step 4: Notice that 8k is divisible by 4 because 8 is a multiple of 4. So, when we divide 8k by 4, the remainder is 0.
Step 5: Now, we only need to consider the 5 when dividing by 4.
Step 6: Divide 5 by 4. The quotient is 1 and the remainder is 1 (because 4 goes into 5 once, leaving 1).
Step 7: 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.
