Understanding Prime Factorization
Prime factorization is the process of expressing a number as a product of its prime numbers. To find the prime factorization of 1600, we will systematically break it down using division.
Step 1: Start with the Number
- Begin with the number 1600.
Step 2: Divide by the Smallest Prime
- The smallest prime number is 2.
- Divide 1600 by 2:
- 1600 ÷ 2 = 800
- Continue dividing by 2:
- 800 ÷ 2 = 400
- 400 ÷ 2 = 200
- 200 ÷ 2 = 100
- 100 ÷ 2 = 50
- 50 ÷ 2 = 25
Step 3: Move to the Next Prime
- Now, 25 is not divisible by 2. Move to the next prime, which is 3.
- 25 is also not divisible by 3.
- The next prime is 5:
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Step 4: Compile the Prime Factors
- We have divided 1600 down to 1.
- The prime factors we have used are:
- 2 (used 6 times)
- 5 (used 2 times)
Final Prime Factorization
- Therefore, the prime factorization of 1600 is:
- 2^6 × 5^2
In conclusion, the prime factorization of 1600 reveals the building blocks of the number using prime numbers, making it easier to understand its properties and relationships in mathematics.