Understanding Divisibility Rules for 1254216

The question asks us to determine which number among the options – 8, 11, 5, and 16 – divides the number 1254216. To solve this, we will apply the divisibility rules for each of these numbers to 1254216.

Divisibility Rule for 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Let's look at the last three digits of 1254216, which are 216.

We need to check if 216 is divisible by 8:

216 \div 8 = 27

Since 216 is divisible by 8, the number 1254216 is also divisible by 8.

Divisibility Rule for 11

A number is divisible by 11 if the alternating sum of its digits (starting from the rightmost digit) is divisible by 11.

For the number 1254216, let's calculate the alternating sum of its digits:

(6 - 1) + (2 - 4) + (5 - 2) + 1 = 5 + (-2) + 3 + 1 = 7 Alternatively: 6 - 1 + 2 - 4 + 5 - 2 + 1 = 7

Since 7 is not divisible by 11, the number 1254216 is not divisible by 11.

Divisibility Rule for 5

A number is divisible by 5 if its last digit is either 0 or 5.

The last digit of 1254216 is 6.

Since the last digit is not 0 or 5, the number 1254216 is not divisible by 5.

Divisibility Rule for 16

A number is divisible by 16 if the number formed by its last four digits is divisible by 16.

Let's look at the last four digits of 1254216, which are 4216.

We need to check if 4216 is divisible by 16:

4216 \div 16 = 263.5

Since 4216 is not perfectly divisible by 16 (it results in a decimal), the number 1254216 is not divisible by 16.

Conclusion on Divisibility

Based on the divisibility rules:

• 1254216 is divisible by 8.
• 1254216 is not divisible by 11.
• 1254216 is not divisible by 5.
• 1254216 is not divisible by 16.

Therefore, the number 1254216 is divisible by 8.