Divisibility Rule For 33 With Examples

Divisibility Rule For 33

The divisibility rule for 33 is based on its prime factors, which are 3 and 11. A number is divisible by 33 if it meets the criteria for both of these factors. Here’s a detailed explanation of how to check for divisibility by 33, along with examples.

Divisibility Rules for 33

To determine if a number is divisible by 33, follow these steps:

1. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
2. Divisibility by 11: A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or divisible by 11.

Combined Rule

For a number to be divisible by 33, it must satisfy both conditions:

• It must be divisible by 3.
• It must be divisible by 11.

Examples

Example 1: Check if 99 is divisible by 33

1. Check for 3:

• Sum of digits: (9 + 9 = 18).
• (18/3 = 6) (no remainder).
• Conclusion: 99 is divisible by 3.

1. Check for 11:

• Odd positions: (9), Even positions: (9).
• Difference: (9 – 9 = 0) (which is divisible by 11).
• Conclusion: 99 is divisible by 11.

Since 99 is divisible by both 3 and 11, it is divisible by 33.

Example 2: Check if 132 is divisible by 33

1. Check for 3:

• Sum of digits: (1 + 3 + 2 = 6).
• (6/3 = 2) (no remainder).
• Conclusion: 132 is divisible by 3.

1. Check for 11:

• Odd positions: (1 + 2 = 3), Even positions: (3).
• Difference: (3 – 3 = 0) (which is divisible by 11).
• Conclusion: 132 is divisible by 11.

Since 132 is divisible by both 3 and 11, it is divisible by 33.

Example 3: Check if 150 is divisible by 33

1. Check for 3:

• Sum of digits: (1 + 5 + 0 = 6).
• (6/3 = 2) (no remainder).
• Conclusion: 150 is divisible by 3.

1. Check for 11:

• Odd positions: (1 + 0 = 1), Even positions: (5).
• Difference: (1 – 5 = -4) (not divisible by 11).
• Conclusion: 150 is not divisible by 11.

Since 150 is not divisible by 11, it is not divisible by 33.

Example 4: Check if 363 is divisible by 33

1. Check for 3:

• Sum of digits: (3 + 6 + 3 = 12).
• (12/3 = 4) (no remainder).
• Conclusion: 363 is divisible by 3.

1. Check for 11:

• Odd positions: (3 + 3 = 6), Even positions: (6).
• Difference: (6 – 6 = 0) (which is divisible by 11).
• Conclusion: 363 is divisible by 11.

Since 363 is divisible by both 3 and 11, it is divisible by 33.

Example 5: Check if 800 is divisible by 33

1. Check for 3:

• Sum of digits: (8 + 0 + 0 = 8).
• (8/3 ≈ 2.67) (not an integer).
• Conclusion: 800 is not divisible by 3.

Since 800 is not divisible by 3, it is not divisible by 33.

Summary

To determine if a number is divisible by 33:

1. Check if it is divisible by 3 (sum of digits is divisible by 3).
2. Check if it is divisible by 11 (difference between the sum of the digits in odd positions and even positions is 0 or divisible by 11).

If a number meets both criteria, it is divisible by 33. This method provides an effective way to assess divisibility for larger numbers.