Understanding Integer Multiples and Divisibility

The video tutorial addresses a math problem from the 2003a ME Too exam, focusing on finding the largest integer multiple of eight with unique digits. The solution involves understanding the constraints, determining the largest possible number, checking divisibility by eight, and calculating the remainder when divided by 1000. The tutorial emphasizes strategic digit arrangement to achieve divisibility.

What is the main objective of the problem discussed in the video?

• To find the greatest integer multiple of 8 with unique digits

• To find the largest prime number less than 1000

• To find the smallest integer multiple of 8

• To find the sum of all digits in a number

How many unique digits can be used to form the number?

• 8

• 10

• 5

• 12

Why is it important to use the largest possible digits in the largest place?

• To minimize the value of the number

• To maximize the value of the number

• To make the number a perfect square

• To make the number divisible by 10

Why is it important to focus on the last three digits of the number?

• Because they determine the number's parity

• Because they determine divisibility by 8

• Because they are the largest digits

• Because they are the smallest digits

What is the largest number with unique digits that can be formed?

• 0987654321

• 8765432109

• 1234567890

• 9876543210

What is the significance of rearranging the digits in the number?

• To increase the number of digits

• To make the number a palindrome

• To make the number smaller

• To ensure the number is divisible by 8

Which of the following combinations of the last three digits is divisible by 8?

• 210

• 231

• 120

• 321

What is the remainder when the number is divided by 1000?

• 100

• 80

• 210

• 120

What is the role of the number 1000 in the problem?

• It is the number of digits allowed

• It is the divisor for finding the remainder

• It is the number to be divided

• It is the largest possible number

What is the correct arrangement of the digits to ensure divisibility by 8?

• 9876543012

• 9876543210

• 9876543120

• 9876543201