Question

a new stadium will have 82,020 seats. the stadium designer wants to divide the seats into sections. each section must have the same number of seats. how many sections could the stadium designer use? select all the possible numbers.

Explanation:

Step1: Check divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3. 82020 ends with 0, so it's divisible by 2. The sum of its digits \(8 + 2+0 + 2+0=12\) is divisible by 3. So 82020 is divisible by 6.

Step2: Check divisibility by 5

A number is divisible by 5 if it ends with 0 or 5. 82020 ends with 0, so it's divisible by 5.

Step3: Check divisibility by 3

The sum of the digits of 82020 is \(8 + 2+0 + 2+0 = 12\), and 12 is divisible by 3. So 82020 is divisible by 3.

Step4: Check divisibility by 4

A number is divisible by 4 if the number formed by its last two - digits is divisible by 4. The last two - digits of 82020 is 20, and 20 is divisible by 4. So 82020 is divisible by 4.

Answer:

6, 5, 3, 4