Divisibility Rule For 23 With Examples

Divisibility Rule For 23

The divisibility rule for 23 is not as straightforward as some other numbers, like 2, 3, or 5, which have simple criteria. However, we can determine if a number is divisible by 23 using some systematic approaches.

Let’s go through the divisibility rule for 23 step-by-step with detailed explanations and multiple examples.

Divisibility Rule for 23

To determine if a number is divisible by 23, we can use the following steps:

1. Identify the Last Digit: Take the last digit of the number.
2. Multiply by 7: Multiply this last digit by 7.
3. Add this product to the Rest of the Number: Remove the last digit from the original number to get the rest of the number, and then add the product from step 2 from this remaining number.
4. Check the Result: If the result is divisible by 23 (including being 0), then the original number is also divisible by 23.

Divisibility Rule for 23

To check if a number is divisible by 23:

1. Identify the last digit of the number.
2. Multiply the last digit by 7.
3. Add this product to the rest of the number.
4. Check if the result is divisible by 23.

Example 1: Check if 184 is divisible by 23

1. Last Digit: 4
2. Multiply by 7: (4 x 7 = 28)
3. Add to the Rest: The rest is 18. So:
   [18 + 28 = 46]
4. Check the Result: 46 is divisible by 23 (as (46/23 = 2)). Thus, 184 is divisible by 23.

Example 2: Check if 529 is divisible by 23

1. Last Digit: 9
2. Multiply by 7: (9 x 7 = 63)
3. Add to the Rest: The rest is 52. So:
   [52 + 63 = 115]
4. Check the Result: 115 is divisible by 23 (as (115/23 = 5)). Thus, 529 is divisible by 23.

Example 3: Check if 1156 is divisible by 23

1. Last Digit: 6
2. Multiply by 7: (6 x 7 = 42)
3. Add to the Rest: The rest is 115. So:
   [115 + 42 = 157]
4. Check the Result: 157 is not divisible by 23 (as (157/23 ≈ 6.82)). Thus, 1156 is not divisible by 23.

Example 4: Check if 1386 is divisible by 23

1. Last Digit: 6
2. Multiply by 7: (6 x 7 = 42)
3. Add to the Rest: The rest is 138. So:
   [138 + 42 = 180]
4. Check the Result: 180 is not divisible by 23 (180 / 23 ≈ 7.83)). Thus, 1386 is not divisible by 23.

Example 1: Check if 184 is divisible by 23

1. Identify the Last Digit: The last digit is 4.
2. Multiply by 7: (4 x 7 = 28).
3. Add to the Rest: The rest is 18 (from 184). Now add:
   [18 + 28 = 46]
4. Check the Result: 46 is divisible by 23. Therefore, 184 is divisible by 23.

Example 2: Check if 299 is divisible by 23

1. Identify the Last Digit: The last digit is 9.
2. Multiply by 7: (9 x 7 = 63).
3. Add to the Rest: The rest is 29. Now add:
   [29 + 63 = 92]
4. Check the Result: 92 is divisible by 23. Therefore, 299 is divisible by 23.

Summary

To determine if a number is divisible by 23, take the last digit and multiply it by 7. Then add that to the rest of the number. If the result is divisible by 23, then the number is divisible by 23.