THINK OF FOUR NUMBERS THAT WILL HAVE A REMAINDER OF 3 WHEN DIVIDED BY 4

Here are four numbers that will have a remainder of 3 when divided by 4:

1. **3**: \( 3 \div 4 \) gives a remainder of 3.
2. **7**: \( 7 \div 4 \) gives a remainder of 3.
3. **11**: \( 11 \div 4 \) gives a remainder of 3.
4. **15**: \( 15 \div 4 \) gives a remainder of 3.

Each of these numbers follows the form \( 4n + 3 \), where \( n \) is an integer.

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Here are 5 related questions:
1. Can you find more numbers that fit the same condition?
2. What is the general formula for numbers that leave a remainder of 3 when divided by 4?
3. What happens when you divide these numbers by 2?
4. Can a negative number have a remainder of 3 when divided by 4?
5. How do you find the remainder when dividing by numbers other than 4?

**Tip**: To find numbers with a specific remainder when divided by any number, use the formula \( divisor \times n + remainder \).

Discover how to find numbers that leave a remainder of 3 when divided by 4 using modular arithmetic. This math problem explores the general formula 4n + 3 and its application to solve remainder problems. Ideal for students in Grades 6-8.

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