Answer
$315 = 3\cdot 3\cdot 5\cdot 7$
Work Step by Step
The $\textit{prime factorization}$ of a number is obtained by writing the number as a product of primes.
To determine the prime factorization of $315$ we write the number as a product of factors and continue the process until all factors are prime numbers.
We start by writing $315$ as a product of two numbers: because the sum of the digits $3+1+5=9$ is divisible by $3$, the number $315$ is divisible by $3$:
$315=3\cdot 105$.
The number $3$ is prime, but $105$ is not. Because the sum of the digits $1+0+5=6$ is divisible by $3$, $105$ is divisible by $3$, so $105=3\cdot 35$:
$315=3\cdot 3\cdot 35$.
As $35$ is not a prime number, we write: $35=5\cdot 7$ and we have:
$315=3\cdot 3\cdot 5\cdot 7$.
Now each factor is a prime number, therefore the prime factorization of $315$ is $3\cdot 3\cdot 5\cdot 7$.
