The prime factorization of 150 is 2 × 3 × 5².
To arrive at this, we start by dividing 150 by the smallest prime number, which is 2. Since 150 is even, we divide:
- 150 ÷ 2 = 75
Next, we take 75 and check for divisibility by the next smallest prime number, which is 3:
- 75 ÷ 3 = 25
Now we have 25, which is not divisible by 3. The next prime number is 5:
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Now that we’ve reached 1, we can compile our prime factors. The factors we found were 2, 3, and 5 (which we counted twice since we divided by 5 two times). Thus, the full prime factorization of 150 is:
2 × 3 × 5 × 5, or written using exponents, 2 × 3 × 5².