Mastering Divisibility Rules: Simplifying Numbers 1 to 10 with Examples
Understanding divisibility rules can demystify the world of numbers and make math much more manageable. In this guide, we’ll walk through the divisibility rules for numbers 1 to 10, and we’ll provide clear examples for each rule.
1. Divisibility by 1: The Universal Divisor Any integer is divisible by 1, regardless of its value.
2. Divisibility by 2: The Even-Odd Test If the last digit of a number is even (0, 2, 4, 6, or 8), the number is divisible by 2.
Examples:
- 146: The last digit is 6 (even), so 146 is divisible by 2.
- 231: The last digit is 1 (odd), so 231 is not divisible by 2.
3. Divisibility by 3: The Digit Sum Criterion If the sum of the digits of a number is divisible by 3, the number itself is divisible by 3.
Examples:
- 183: Digit sum = 1 + 8 + 3 = 12 (divisible by 3), so 183 is divisible by 3.
- 427: Digit sum = 4 + 2 + 7 = 13 (not divisible by 3), so 427 is not divisible by 3.
4. Divisibility by 4: The Last Two Digits Rule If the two-digit number formed by the last two digits of a number is divisible by 4, the whole number is divisible by 4.
Examples:
- 932: The last two digits, 32, are divisible by 4, so 932 is divisible by 4.
- 675: The last two digits, 75, are not divisible by 4, so 675 is not divisible by 4.
5. Divisibility by 5: The Zero or Five Check If the last digit of a number is 0 or 5, the number is divisible by 5.
Examples:
- 540: The last digit is 0, so 540 is divisible by 5.
- 763: The last digit is 3, so 763 is not divisible by 5.
6. Divisibility by 6: The Combo Rule A number is divisible by 6 if it is divisible by both 2 and 3.
Examples:
- 342: Divisible by 2 (last digit is even) and by 3 (digit sum = 3 + 4 + 2 = 9), so 342 is divisible by 6.
- 516: Divisible by 2 (last digit is even) but not by 3 (digit sum = 5 + 1 + 6 = 12), so 516 is not divisible by 6.
7. Divisibility by 7: The Division Dilemma Divisibility by 7 is trickier and often requires direct division or more advanced methods.
8. Divisibility by 8: The Last Three Digits Criterion If the three-digit number formed by the last three digits of a number is divisible by 8, the whole number is divisible by 8.
Examples:
- 2488: The last three digits, 488, are divisible by 8, so 2488 is divisible by 8.
- 7315: The last three digits, 315, are not divisible by 8, so 7315 is not divisible by 8.
9. Divisibility by 9: The Digit Sum Redux Similar to divisibility by 3, if the sum of the digits is divisible by 9, the number itself is divisible by 9.
Examples:
- 621: Digit sum = 6 + 2 + 1 = 9 (divisible by 9), so 621 is divisible by 9.
- 478: Digit sum = 4 + 7 + 8 = 19 (not divisible by 9), so 478 is not divisible by 9.
10. Divisibility by 10: The Trailing Zero Principle Any number ending with 0 is divisible by 10.
Examples:
- 930: Ends with 0, so 930 is divisible by 10.
- 742: Does not end with 0, so 742 is not divisible by 10.
Mastering these divisibility rules can significantly simplify your math computations, whether you’re working with small or large numbers. By applying these rules and practicing with various examples, you’ll gain a valuable tool for your mathematical toolkit.