To determine if the first number is divisible by the second, you must perform division and check for a remainder; if there is no remainder, the first number is divisible by the second.
Understanding Divisibility
Divisibility is a mathematical concept indicating whether one number can be divided by another number without leaving any remainder. In simpler terms, a number is divisible by another if the division operation results in a whole number quotient.
The Division Process
The core of determining divisibility lies in the process of division. You divide the first number (dividend) by the second number (divisor). If the division results in a whole number (no fractional part or decimal), then the first number is divisible by the second. If there is a remainder, then the first number is not divisible by the second.
Methods to Check Divisibility
Simple Division
The primary method is to perform the division operation directly. If the result of the division is a whole number, the first number is divisible by the second.
- Example 1: 12 ÷ 2 = 6. There is no remainder; thus, 12 is divisible by 2.
- Example 2: 12 ÷ 5 = 2.4. This division results in a decimal, and there is a remainder, so 12 is not divisible by 5.
The Remainder Check
Based on the reference provided, "if you can divide two numbers without a remainder, then the first number is divisible by the second."
- If the remainder is zero: The first number is divisible by the second.
- If the remainder is not zero: The first number is not divisible by the second.
Example Table
| First Number (Dividend) | Second Number (Divisor) | Result of Division | Remainder | Divisible? |
|---|---|---|---|---|
| 12 | 2 | 6 | 0 | Yes |
| 12 | 5 | 2.4 | 2 | No |
| 15 | 3 | 5 | 0 | Yes |
| 16 | 5 | 3.2 | 1 | No |
Practical Insights
- Even Numbers: Any even number is divisible by 2 since when divided by two, there is no remainder.
- Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5.
- Divisibility by 10: A number is divisible by 10 if its last digit is 0.
Conclusion
To determine whether the first number is divisible by the second, simply divide the first number by the second. If the result is a whole number (or equivalently, if there is no remainder), then the first number is divisible by the second; otherwise, it is not.
