4. An infinite geometric progression consists of natural numbers. It turned out that the product of the first four terms equals param1. Find the number of such progressions.

The infinite geometric progression consists of positive integers. It turned out that the product of the first four terms equals param1. Find the number of such progressions.

| param1 | Answer |
| :---: | :---: |
| $2^{200} 3^{300}$ | 442 |
| $2^{200} 5^{400}$ | 578 |
| $3^{200} 5^{600}$ | 867 |
| $2^{300} 7^{600}$ | 1326 |
| $3^{300} 7^{500}$ | 1092 |

## Condition

An infinite geometric progression consists of natural numbers. It turned out that the product of the first four terms equals $2^{200} 3^{300}$. Find the number of such progressions.

## Answer.

442