Step-by-Step Instructions
Choose a Number
First, identify the number you want to check for divisibility. This can be any integer.
Apply the Divisibility Rules
Next, apply each divisibility rule from 2 to 13 to your chosen number, checking which rules the number satisfies.
Work Through Each Rule
For each rule, perform the required operation (such as summing digits or checking the last digit) to determine if your number is divisible by that number.
Record the Results
Keep track of which numbers your chosen integer is divisible by, based on the rules applied in the previous steps.
Double-Check Calculations
Review your work to ensure accuracy, especially when applying rules for larger divisors like 11 and 13, which can be more complex.
Consider Using a Calculator for Verification
If you're working with large numbers or need to verify your results quickly, consider using a divisibility calculator as a final step to confirm your findings.
Introduction to Divisibility
Divisibility rules help determine if a number can be divided evenly by another number. In this guide, we will cover the divisibility rules for numbers 2 through 13.
Understanding the Rules
Each number has its own divisibility rule. For example, a number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). A number is divisible by 3 if the sum of its digits is divisible by 3.
List of Divisibility Rules
- 2: Last digit is even (0, 2, 4, 6, or 8)
- 3: Sum of digits is divisible by 3
- 4: Last two digits form a number divisible by 4
- 5: Last digit is 0 or 5
- 6: Number is divisible by both 2 and 3
- 7: Double the last digit and subtract this value from the remaining digits; if the result is divisible by 7, then the original number is divisible by 7
- 8: Last three digits form a number divisible by 8
- 9: Sum of digits is divisible by 9
- 10: Last digit is 0
- 11: Alternate sum of digits is divisible by 11
- 12: Number is divisible by both 3 and 4
- 13: Add 4 times the last digit to the remaining digits; if the result is divisible by 13, then the original number is divisible by 13
Worked Example
Let's say we want to check the divisibility of the number 936.
- For 2: Last digit is 6, which is even, so 936 is divisible by 2.
- For 3: Sum of digits is 9 + 3 + 6 = 18, which is divisible by 3, so 936 is divisible by 3.
- For 4: Last two digits (36) form a number divisible by 4, so 936 is divisible by 4.
- For 5: Last digit is not 0 or 5, so 936 is not divisible by 5.
- Continuing this process for all numbers up to 13, we can determine which numbers divide 936 evenly.
Common Mistakes to Avoid
- Forgetting to check each divisibility rule individually
- Incorrectly applying the rules, such as mistaking the divisibility rule for one number with another
- Not using the rules for larger numbers, thinking they are only for small numbers
When to Use a Calculator
While it's good to know how to perform these calculations by hand, using a divisibility calculator can be convenient when:
- Working with very large numbers
- Needing to check divisibility for many numbers at once
- Looking for a quick verification of your manual calculations