If a number leaves a remainder of 7 when divided by 10, what will be the remaind

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Question: If a number leaves a remainder of 7 when divided by 10, what will be the remainder when the same number is divided by 5?

Options:

Correct Answer: 2

Solution:

The number can be expressed as 10k + 7. When divided by 5, the remainder is 7 mod 5, which is 2.

If a number leaves a remainder of 7 when divided by 10, what will be the remainder when the same number is divided by 5?

If a number leaves a remainder of 7 when divided by 10, what will be the remainder when the same number is divided by 5?

Step 1: Understand that if a number leaves a remainder of 7 when divided by 10, it can be written in the form of 10k + 7, where k is any whole number.
Step 2: Now, we need to find the remainder of this number (10k + 7) when it is divided by 5.
Step 3: Divide 10k by 5. Since 10 is a multiple of 5, 10k divided by 5 leaves a remainder of 0.
Step 4: Now, consider the remainder of 7 when divided by 5. When you divide 7 by 5, it goes 1 time with a remainder of 2.
Step 5: Combine the results from Step 3 and Step 4. The total remainder when (10k + 7) is divided by 5 is 0 (from 10k) + 2 (from 7), which equals 2.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Divisibility Rules – Applying rules for division and remainders to solve problems.