Understanding Prime Factorization
Prime factorization involves expressing a number as the product of its prime factors. To find the prime factorization of 2560, we can use the method of repeated division by prime numbers.
Step-by-Step Prime Factorization of 2560
1. Divide by the smallest prime number
- 2560 is even, so we start with 2.
- 2560 ÷ 2 = 1280
2. Continue dividing by 2
- 1280 ÷ 2 = 640
- 640 ÷ 2 = 320
- 320 ÷ 2 = 160
- 160 ÷ 2 = 80
- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
3. Identify remaining prime number
- We can no longer divide by 2 since 5 is odd. The next prime number is 5.
- 5 ÷ 5 = 1
Compile the Prime Factors
- The prime factors obtained from the divisions are:
- 2 (appears 8 times)
- 5 (appears 1 time)
Final Prime Factorization of 2560
- Therefore, the prime factorization of 2560 can be expressed as:
- 2560 = 2^8 × 5^1
This detailed breakdown shows how each step leads to the final result, demonstrating the systematic approach to prime factorization.