Divisibility Tricks and Tests

The video discusses the challenge of determining if a number is divisible by 7 and introduces a trick to simplify this process. The trick involves manipulating the digits of a number and checking if the result is divisible by 7. An alternative method is also presented, along with an explanation of why the trick works. The video highlights practical applications of knowing divisibility by 7 and recaps divisibility tests for numbers 1 to 12. It concludes with a sponsor message.

What is the first step in the trick to determine if a number is divisible by 7?

• Subtract the last digit from the rest of the number

• Remove the last digit and multiply it by 5

• Multiply the entire number by 5

• Add all the digits together

In the alternative method for checking divisibility by 7, what operation is performed after removing the last digit?

• Subtract twice the last digit from the rest

• Multiply the last digit by 3 and subtract

• Multiply the last digit by 5 and add

• Add twice the last digit to the rest

Why might it be useful to know if a number is divisible by 7?

• To determine the prime factors of a number

• To calculate the area of a circle

• To split a bill among 7 people

• To solve quadratic equations

Which of the following numbers is divisible by 2?

• 42

• 23

• 15

• 57

What is the test for divisibility by 9?

• Check if the number ends in 9

• Add all the digits and see if the sum is divisible by 9

• Multiply the last digit by 9

• Subtract 9 from the number

How can you determine if a number is divisible by 3?

• Check if the number is even

• Add all the digits and see if the sum is divisible by 3

• Multiply the last digit by 3

• Subtract 3 from the number

What is the alternating sum test used for?

• Divisibility by 8

• Divisibility by 6

• Divisibility by 11

• Divisibility by 5

To check if a number is divisible by 6, which two tests must it pass?

• Divisibility by 4 and 5

• Divisibility by 3 and 9

• Divisibility by 5 and 10

• Divisibility by 2 and 3

What is the divisibility test for 4?

• Check if the last digit is 4

• Check if the last two digits form a number divisible by 4

• Add all digits and check if the sum is divisible by 4

• Multiply the last digit by 4

What is the main focus of the sponsor message at the end of the video?

• A new mathematical theorem

• An internship program at Jane Street

• A recap of divisibility rules

• A new video series on Numberphile