Divisibility Rule For 24 With Examples
Divisibility Rule For 24 With Examples
Divisibility Rule For 24
The divisibility rule for 24 can be derived from its prime factors. Since (24 = 2^3 x 3), a number must be divisible by both (8) and (3) to be divisible by (24).
Divisibility Rules for 24
- Divisibility by 8: A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Combining the Rules
For a number to be divisible by 24, it must satisfy both conditions above.
The divisibility rule for 24 relies on checking divisibility by its prime factors, specifically (8) and (3), since (24 = 2^3 x 3). Here’s how we can determine if a number is divisible by 24:
Divisibility Rules for 24
- Divisibility by 8: A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Combined Rule
For a number to be divisible by 24, it must satisfy both conditions:
- It must be divisible by 8.
- It must be divisible by 3.
Examples
Example 1: Check if 192 is divisible by 24
- Check for 8:
- Last three digits: 192
- (192/8 = 24) (no remainder)
- Conclusion: 192 is divisible by 8.
- Check for 3:
- Sum of digits: (1 + 9 + 2 = 12)
- (12/3 = 4) (no remainder)
- Conclusion: 192 is divisible by 3.
Since 192 is divisible by both 8 and 3, it is divisible by 24.
Example 2: Check if 150 is divisible by 24
- Check for 8:
- Last three digits: 150
- (150/8 = 18.75) (remainder present)
- Conclusion: 150 is not divisible by 8.
Since 150 is not divisible by 8, it is not divisible by 24.
Example 3: Check if 288 is divisible by 24
- Check for 8:
- Last three digits: 288
- (288/8 = 36) (no remainder)
- Conclusion: 288 is divisible by 8.
- Check for 3:
- Sum of digits: (2 + 8 + 8 = 18)
- (18/3 = 6) (no remainder)
- Conclusion: 288 is divisible by 3.
Since 288 is divisible by both 8 and 3, it is divisible by 24.
Example 4: Check if 100 is divisible by 24
- Check for 8:
- Last three digits: 100
- (100/8 = 12.5) (remainder present)
- Conclusion: 100 is not divisible by 8.
Since 100 is not divisible by 8, it is not divisible by 24.
Example 5: Check if 720 is divisible by 24
- Check for 8:
- Last three digits: 720
- (720/8 = 90) (no remainder)
- Conclusion: 720 is divisible by 8.
- Check for 3:
- Sum of digits: (7 + 2 + 0 = 9)
- (9/3 = 3) (no remainder)
- Conclusion: 720 is divisible by 3.
Since 720 is divisible by both 8 and 3, it is divisible by 24.
Examples
Example 1: Check if 432 is divisible by 24
- Check for 8:
- Last three digits: 432
- (432/8 = 18) (no remainder)
- So, 432 is divisible by 8.
- Check for 3:
- Sum of digits: (4 + 3 + 2 = 9)
- (9/3 = 3) (no remainder)
- So, 432 is divisible by 3.
Since 432 is divisible by both 8 and 3, it is divisible by 24.
Example 2: Check if 161 is divisible by 24
- Check for 8:
- Last three digits: 161
- (161/8 = 20.12) (remainder present)
- So, 161 is not divisible by 8.
Since 161 is divisible by 8, it is not divisible by 24.
Example 3: Check if 264 is divisible by 24
- Check for 8:
- Last three digits: 264
- (264/8 = 33) (no remainder)
- So, 288 is divisible by 8.
- Check for 3:
- Sum of digits: (2 + 6 + 4 = 12)
- (12/3 = 4) (no remainder)
- So, 264 is divisible by 3.
Since 264 is divisible by both 8 and 3, it is divisible by 24.
Example 4: Check if 205 is divisible by 24
- Check for 8:
- Last three digits: 205
- (205/8 = 25.6) (remainder present)
- So, 205 is not divisible by 8.
Since 205 is not divisible by 8, it is not divisible by 24.
Summary
To determine if a number is divisible by 24:
- Check if it is divisible by 8 (last three digits).
- Check if it is divisible by 3 (sum of digits).
- If both conditions are satisfied, the number is divisible by 24. This method is efficient and straightforward for checking divisibility.