Real-world Applications of Integer Factorization

Question

All of us know the extensive application of integer factorization in Cryptography. But, I would like to know its applications in other fields.

If anyone knows some applications of integer factorization with applications in data science or data mining. Please state them as well.

Answer 1

The field of Combinatorics.

---

For example:

Find the number of positive integer divisors of $48$.

---

Using the prime factorization of $48=2^4\cdot3^1$, we can easily answer this question:

• In each divisor, the factor $2$ can appear between $0$ and $4$ times, i.e., $5$ different combinations
• In each divisor, the factor $3$ can appear between $0$ and $1$ times, i.e., $2$ different combinations

Hence there are $5\cdot2=10$ divisors:

• $2^0\cdot3^0$
• $2^0\cdot3^1$
• $2^1\cdot3^0$
• $2^1\cdot3^1$
• $2^2\cdot3^0$
• $2^2\cdot3^1$
• $2^3\cdot3^0$
• $2^3\cdot3^1$
• $2^4\cdot3^0$
• $2^4\cdot3^1$