If a number leaves a remainder of 2 when divided by 5, which of the following nu

If a number leaves a remainder of 2 when divided by 5, which of the following numbers will also leave the same remainder when divided by 5? (2023)

If a number leaves a remainder of 2 when divided by 5, which of the following numbers will also leave the same remainder when divided by 5? (2023)

Step 1: Understand what it means for a number to leave a remainder of 2 when divided by 5. This means that when you divide the number by 5, the leftover amount after the division is 2.
Step 2: Write the condition mathematically. If a number 'x' leaves a remainder of 2 when divided by 5, we can express this as x = 5k + 2, where 'k' is any whole number (0, 1, 2, ...).
Step 3: Check the number 2023. To find out if it leaves a remainder of 2 when divided by 5, divide 2023 by 5.
Step 4: Calculate 2023 divided by 5. The result is 404 with a remainder of 3 (because 5 * 404 = 2020 and 2023 - 2020 = 3).
Step 5: Since 2023 leaves a remainder of 3, it does not satisfy the condition of leaving a remainder of 2 when divided by 5.
Step 6: Now, check other numbers to see if they leave a remainder of 2 when divided by 5. For example, check 17.
Step 7: Divide 17 by 5. The result is 3 with a remainder of 2 (because 5 * 3 = 15 and 17 - 15 = 2).
Step 8: Since 17 leaves a remainder of 2, it satisfies the condition.

Modular Arithmetic – Understanding how remainders work when dividing numbers, specifically focusing on the concept of congruences.