A student divides a number by 6 and gets a remainder of 4. If he divides the sam

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Question: A student divides a number by 6 and gets a remainder of 4. If he divides the same number by 3, what will be the remainder? (2023)

Options:

Correct Answer: 4

Exam Year: 2023

Solution:

If the number is of the form 6k + 4, when divided by 3, it gives a remainder of 1 (4 % 3 = 1).

A student divides a number by 6 and gets a remainder of 4. If he divides the same number by 3, what will be the remainder? (2023)

A student divides a number by 6 and gets a remainder of 4. If he divides the same number by 3, what will be the remainder? (2023)

Step 1: Understand that when a number is divided by 6 and gives a remainder of 4, it can be expressed in the form of 6k + 4, where k is any whole number.
Step 2: Recognize that we need to find the remainder when this number (6k + 4) is divided by 3.
Step 3: Break down the expression 6k + 4 into two parts: 6k and 4.
Step 4: Notice that 6k is divisible by 3, so it gives a remainder of 0 when divided by 3.
Step 5: Now, focus on the 4. When you divide 4 by 3, you get a quotient of 1 and a remainder of 1 (because 4 = 3 * 1 + 1).
Step 6: Combine the results: since 6k gives a remainder of 0 and 4 gives a remainder of 1, the total remainder when dividing 6k + 4 by 3 is 0 + 1 = 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers by different divisors.
Number Representation – Expressing numbers in terms of their divisors to analyze their properties.