To find the prime factorization of 40, we begin by identifying the smallest prime number that can divide it, which is 2. We can repeatedly divide the number by 2 until it can no longer be divided evenly.
- First division: 40 ÷ 2 = 20
- Second division: 20 ÷ 2 = 10
- Third division: 10 ÷ 2 = 5
At this stage, we’ve divided 40 by 2 three times, and we have reached the number 5, which is itself a prime number.
Now we can summarize our findings:
- We have divided by 2 three times, which contributes 23 to the factorization.
- We have the prime number 5 that we reached as a result of the divisions.
Combining these, we can express the prime factorization of 40 as:
23 × 5
In conclusion, the prime factorization of 40 is 23 × 5. This means that if you multiply 2 by itself three times (2 × 2 × 2) and then multiply that result by 5, you’ll get back to 40.