How do you know if a number is divisible by 11 and 12?

To determine if a number is divisible by 11 and 12, you need to check if it satisfies the divisibility rules for both numbers.

Divisibility by 11

The divisibility rule for 11 states that a number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.

Steps to check divisibility by 11:

1. Sum the digits at odd places (from right to left).
2. Sum the digits at even places (from right to left).
3. Calculate the difference between the two sums (larger sum minus smaller sum).
4. If the difference is 0 or a multiple of 11, the number is divisible by 11.

Example:

Consider the number 918,082.

1. Sum of digits at odd places (2 + 0 + 1) = 3
2. Sum of digits at even places (8 + 8 + 9) = 25
3. Difference = 25 - 3 = 22
4. Since 22 is a multiple of 11, 918,082 is divisible by 11.

Divisibility by 12

The divisibility rule for 12 states that a number is divisible by 12 if it is divisible by both 3 and 4.

Steps to check divisibility by 12:

1. Check divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
2. Check divisibility by 4: A number is divisible by 4 if its last two digits are divisible by 4.

Example:

Consider the number 732.

1. Divisibility by 3: 7 + 3 + 2 = 12. 12 is divisible by 3, so 732 is divisible by 3.
2. Divisibility by 4: The last two digits are 32. 32 is divisible by 4, so 732 is divisible by 4.

Since 732 is divisible by both 3 and 4, it is divisible by 12.

In summary:

A number is divisible by both 11 and 12 if it satisfies both divisibility rules:

• The difference between the sum of digits at odd and even places is 0 or a multiple of 11.
• The number is divisible by both 3 and 4.