Prime factorization

Number Theory Level 1

What is the smallest positive integer $x$ such that

$x = \text{Prime} \times \text{Prime} \times \text{Prime} \times \text{Prime}?$

Note: The prime numbers are not necessarily distinct.

Here is a similar problem.

2 solutions

Munem Shahriar
Nov 19, 2017

The smallest prime number is 2

Hence $x = 2^4 = \boxed{16}$

Nazmus Sakib
Nov 19, 2017

Smallest prime number is $2$ also given that the prime numbers are not distinct.

From this equation

$x = \text{Prime} \times \text{Prime} \times \text{Prime} \times \text{Prime}?$

the product of 4 same smallest prime number is equal to the smallest positive integer

So, Now we get,

$x = 2\times 2\times2 \times 2$

$x=16$