43x47

The Prime Factorization of 2021 is 43 x 47.

Let's start with some definitions for this one. 

• prime: A prime number can only be divided by itself and 1. Examples: 3, 5, 7, 19
• factor: Factors are the numbers you multiply together to get another number. Examples: 3, 6 and 12 are some (not all!) factors of 36 because 3 x 12 = 36 and 6 x 6 = 36. 

Prime factorization means breaking down a number into a list of all its prime factors. A few examples:

• 15 = 3 x 5
• 28 = 2 x 2 x 7 (Note that 4 x 7 is incorrect because 4 is not prime)

Can you come up with a different way to multiply only prime numbers to get 15? or 28? I know I can't! Prime factorization is unique - that means for every single whole number, there is only one way to break it into prime factors. Changing the order doesn't count (3 x 5 is the same as 5 x 3) and repeats do count (2 x 7 is not equal to 2 x 2 x 7).

For a more detailed explanation of prime factorization with more examples, see MathIsFun.

Reason to 'Prime Factorize'

Since prime numbers cannot be divided by anything except themselves and 1, they can operate as 'building blocks' for different fields of math. Cryptography is the science of secret codes, and relies on very, very large prime numbers to make those secret codes almost unbreakable.

For very big numbers, it is tough to computers (and people!) to figure out if a number is prime- and if not, what are its factors? In fact, several groups are offering cash prizes to those who can discover a new prime with more than one hundred digits.

Further Reading

News Article about Primes and Encryption, from ABC.net

Is 1 prime? Find out why it is not at Scientific American

GIMPS - Great Internet Mersenne Prime Search