The video introduces number theory, focusing on integers and their properties. It covers basic concepts like divisibility and the greatest common factor (GCF), using examples to illustrate these ideas. The video also explores linear combinations and their relation to GCF, using a ruler problem to demonstrate practical applications. Finally, it discusses cryptography, highlighting the role of prime numbers in securing information and the challenges of factorization.

What is the primary focus of number theory?

• The study of fractions

• The study of irrational numbers

• The study of integers

• The study of decimals

What is the smallest positive integer you can achieve from a linear combination of two numbers?

• The sum of the two numbers

• The product of the two numbers

• The greatest common factor of the two numbers

• The difference between the two numbers

How can you measure a distance of 2 centimeters using 7 cm and 5 cm rulers?

• By adding the lengths of both rulers

• By subtracting the 5 cm ruler from the 7 cm ruler

• By using only the 7 cm ruler

• By using only the 5 cm ruler

What is the greatest common factor of 91 cm and 26 cm ruler lengths?

• 1

• 13

• 26

• 91

Why are large prime numbers important in cryptography?

• They are difficult to factor

• They are easy to factor

• They are used to add numbers

• They are used to subtract numbers

What is a potential flaw in using a secret key for encryption?

• The key can be found using the greatest common factor

• The key can be easily guessed

• The key is too small

• The key is too large

What is the fastest known algorithm for factoring large numbers?

• The quick sort algorithm

• The Euclidean algorithm

• The general number field sieve

• The bubble sort algorithm