Divisibility Rule For 16 With Examples

Divisibility Rule for 16

A number is divisible by 16 if the number formed by its last four digits is divisible by 16. This means we only need to focus on the last four digits of the number to determine divisibility.

Steps to Check Divisibility by 16

1. Identify the Last Four Digits: Take the last four digits of the number. If the number has fewer than four digits, use all of them.
2. Check Divisibility by 16: Divide this four-digit (or fewer) number by 16. If the result is an integer (i.e., there’s no remainder), then the original number is divisible by 16.

Example Walkthroughs

Example 1: 2,048

1. Identify the Last Four Digits: 2048 (all digits since it has four).
2. Check Divisibility by 16:

• (2048/16 = 128) (with no remainder).

1. Final Conclusion: Since there is no remainder, 2048 is divisible by 16.

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Example 2: 12,736

1. Identify the Last Four Digits: 736.
2. Check Divisibility by 16:

• (736/16 = 46) (with no remainder).

1. Final Conclusion: Since there is no remainder, 12,736 is divisible by 16.

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Example 3: 9,220

1. Identify the Last Four Digits: 9220.
2. Check Divisibility by 16:

• (9220/16 = 577.5) (not an integer, remainder exists).

1. Final Conclusion: Since there is a remainder, 9,220 is not divisible by 16.

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Example 4: 1,024

1. Identify the Last Four Digits: 1024 (all digits since it has four).
2. Check Divisibility by 16:

• (1024/16 = 64) (with no remainder).

1. Final Conclusion: Since there is no remainder, 1,024 is divisible by 16.

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Example 5: 5,000

1. Identify the Last Four Digits: 5000.
2. Check Divisibility by 16:

• (5000/16 = 312.5) (not an integer, remainder exists).

1. Final Conclusion: Since there is a remainder, 5,000 is not divisible by 16.

1. Example 1: 123456
   • Last four digits: 3456
   • Check: 3456÷16 = 216 (remainder 0)
   • Conclusion: 123456 is divisible by16.
2. Example 2: 987654321
   • Last four digits: 4321
   • Check: 4321÷16 = 270.062 (remainder is not 0)
   • Conclusion: 987654321 is not divisible by 16.
3. Example 3: 256
   • Last four digits: 0256 (or just 256)
   • Check: 256÷16 = 16 (remainder 0)
   • Conclusion: 256 is divisible by 16.
4. Example 4: 10000
   • Last four digits: 0000
   • Check: 0÷16 = 0(remainder 0)
   • Conclusion: 10000 is divisible by 16.

Example 1: 24,432

• Last four digits: 4432
• Check: 4432÷16 = 277
• Since 277 is a whole number, 24,432 is divisible by 16.

Example 2: 1,234,568

• Last four digits: 8568
• Check: 8568÷16 = 535.5
• Since this is not a whole number, 1,234,568 is not divisible by 16.

Example 3: 100,000

• Last four digits: 0000
• Check: 0000÷16 = 0
• Since 0 is a whole number, 100,000 is divisible by 16.

Example 4: 5,376

• Last four digits: 5376
• Check: 5376÷16 = 336
• Since 336 is a whole number, 5,376 is divisible by 16.

Summary

To determine if a number is divisible by 16:

• Focus on the last four digits of the number.
• Divide this number by 16.
• If the result is an integer (no remainder), then the original number is divisible by 16.

This method is efficient for checking divisibility by 16, particularly for large numbers.

By applying this rule, we can quickly determine if larger numbers are divisible by 16 without doing extensive calculations.