Understanding Friendly and Solitary Numbers

The video explores the concept of friendly numbers, which are numbers that share the same index, calculated by dividing the sum of their factors by the number itself. It compares friendly numbers to perfect numbers, which have an index of 2. The video also discusses solitary numbers, which do not have a friend with the same index, and highlights the mystery surrounding the number 10, as it is unknown whether it is solitary or friendly. The video is set against the backdrop of Numberphile's 10th anniversary.

What is the significance of the number 10 in the context of the video?

• It is a prime number.

• It is a perfect number.

• It is the 10th anniversary of the channel.

• It is the first number discussed in the video.

What is the index of a number in the context of friendly numbers?

• The sum of its factors divided by the number itself.

• The difference between the number and its factors.

• The number of factors it has.

• The product of its factors.

Which of the following is a characteristic of perfect numbers?

• Their index is exactly 2.

• They have no factors.

• They are always prime numbers.

• Their index is less than 1.

What is a key difference between friendly and perfect numbers?

• Perfect numbers have no factors.

• Friendly numbers do not need an integer index.

• Friendly numbers are always prime.

• Perfect numbers have an index of 1.

What is a solitary number?

• A number with infinite friends.

• A number with an index of 1.

• A number with no friends.

• A number that is a perfect square.

Why are prime numbers considered solitary?

• They have no factors.

• They have an index of 2.

• Their index does not cancel down.

• They are always even.

Which of the following numbers is known to be friendly?

• 12

• 5

• 25

• 18

What is the significance of the number 18 in the context of solitary numbers?

• It has infinite friends.

• It is solitary despite having a reducible index.

• It is a perfect number.

• It is a prime number.

What is the index of the number 10?

• 1.8

• 2.0

• 1.5

• 2.5

What is the main challenge in finding a friend for the number 10?

• No number with the same index has been found yet.

• 10 is a prime number.

• 10 is a perfect number.

• 10 has no factors.