Divisibility Rules and Tests

The video discusses the complexity of determining divisibility by 7 and introduces a unique trick to simplify the process. The trick involves manipulating the last digit of a number and checking if the result is divisible by 7. The video also presents an alternative method and explains the mathematical reasoning behind the trick. Practical applications of knowing divisibility by 7 are discussed, followed by a recap of divisibility tests for numbers 1 to 12. The video concludes with a sponsor message.

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

• Multiply the entire number by 5

• Add all the digits together

• Remove the last digit and multiply it by 5

• Divide the number by 2

If the result of the divisibility test for 7 is not divisible by 7, what can be concluded about the original number?

• The original number is even

• The original number is a prime number

• The original number is not divisible by 7

• The original number is divisible by 7

What is the alternative method for checking divisibility by 7?

• Divide the number by 3

• Multiply the last digit by 10

• Subtract twice the last digit from the rest of the number

• Add the last digit to the rest of the number

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

• To calculate the area of a circle

• To find the square root of a number

• To split a bill among 7 people

• To determine if a number is prime

Which of the following numbers is divisible by 2?

• 15

• 22

• 49

• 37

What is the test for divisibility by 9?

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

• Check if the number ends in 9

• Subtract 9 from the number

• Multiply the number by 9

How can you determine if a number is divisible by 11?

• Add all the digits together

• Multiply the number by 11

• Check if the number is even

• Alternate adding and subtracting the digits

What two tests must a number pass to be divisible by 6?

• Divisibility by 2 and 3

• Divisibility by 5 and 10

• Divisibility by 4 and 5

• Divisibility by 3 and 9

What is the focus of Jane Street's support for Numberphile?

• To host a mathematics competition

• To advertise their new product line

• To encourage creative and curious individuals to join their team

• To promote their new book

What humorous difficulty does the speaker mention at the end of the video?

• Remembering the times table

• Pronouncing 'divisibility'

• Solving a complex equation

• Understanding a math joke