Prime Factorization of 5005 and Number System Chart

Prime factorization means breaking down a composite number into a product of purely prime numbers (numbers divisible only by 1 and themselves, like 2, 3, 5, 7, 11).

Step-by-Step Solution for 5005:

1. It ends in 5, so it is not divisible by 2. It is not divisible by 3 (sum of digits is 10). Let's divide by 5.
   • $5005 / 5 = 1001$
2. Now we have 1001. It is not divisible by 5. Let's check the next prime, 7.
   • $1001 / 7 = 143$
3. Now we have 143. Check the next prime, 11.
   • $143 / 11 = 13$
4. 13 is a prime number itself, so it is only divisible by 13.
   • $13 / 13 = 1$

Final Answer: The prime factorization of 5005 is 5 × 7 × 11 × 13.

In mathematics, numbers are classified into a hierarchy:

1. Natural Numbers (N): Counting numbers (1, 2, 3...).
2. Whole Numbers (W): Natural numbers + Zero (0, 1, 2, 3...).
3. Integers (Z): Whole numbers + Negative numbers (...-2, -1, 0, 1, 2...).
4. Rational Numbers (Q): Any number that can be written as a fraction p/q (e.g., 1/2, 0.75, 5).
5. Irrational Numbers: Numbers that cannot be written as simple fractions (e.g., √2, π).
6. Real Numbers (R): The combination of ALL Rational and Irrational numbers.