Factorization

Multiply these numbers

491 x 673

This number is the product of two numbers. What are they? \[ 1247 = a \times b \]

This number is the product of two numbers. What are they? \[ 80851 = c \times d \]

RSA-2048 cryptography is based on the difficulty of a problem like this:

I generate two large, random prime numbers, \(p\) and \(q\), each of length 1024 bits. I then give you the product \[ n=p \times q \]

Find \(p\) and \(q\).