Understanding Simplest Form
To simplify the number 4845, we need to express it in its simplest form, often referred to as finding the prime factorization or the greatest common factor (GCF) and reducing it.
Step 1: Prime Factorization
- Begin by dividing 4845 by the smallest prime number.
- Check if it's divisible by 3 (the sum of digits is 21, which is divisible by 3):
- 4845 ÷ 3 = 1615
- Now, factor 1615:
- Check if it's divisible by 5 (it ends in 5):
- 1615 ÷ 5 = 323
- Now, factor 323:
- Check divisibility by 17 (323 ÷ 17 = 19):
- 323 = 17 × 19
Step 2: Combine the Factors
- The prime factorization of 4845 is 3 × 5 × 17 × 19.
Step 3: Expressing in Simplest Form
- Since 4845 is already a whole number and does not have any common factors with any other number unless specified, we can conclude that the simplest form of a whole number is the number itself.
- Thus, the simplest form of 4845 is 4845.
Conclusion
- The number 4845 is already in its simplest form and cannot be reduced further without changing its value.
- Understanding prime factorization helps in various mathematical calculations, ensuring a strong foundation in number theory.
By breaking down the number into its prime components, we can better understand its structure and relationships with other numbers.