To find the prime factorization of 162, we begin by dividing it by the smallest prime number, which is 2. Since 162 is even, we start there:
- 162 ÷ 2 = 81
Next, we look at 81. The next smallest prime number is 3. We divide:
- 81 ÷ 3 = 27
We can divide 27 by 3 again:
- 27 ÷ 3 = 9
Continuing with 9, we divide by 3:
- 9 ÷ 3 = 3
Finally, we divide the last 3 by itself:
- 3 ÷ 3 = 1
Now, we can list out all the prime factors we used in this process:
- 2 from the first division
- 3 from the second division (used three times)
So, the complete prime factorization of 162 is:
- 2 × 3 × 3 × 3 × 3, or you can also represent it using exponents as 2 × 34.