Understanding the Divisibility of 4845
To determine what can be divided into 4845, we first need to find its factors. A factor is a number that divides another number without leaving a remainder.
Finding Factors of 4845
- Prime Factorization: Start by breaking down 4845 into its prime factors.
- 4845 is odd, so it's not divisible by 2.
- Check for divisibility by 3: The sum of the digits (4 + 8 + 4 + 5 = 21) is divisible by 3.
- 4845 ÷ 3 = 1615
- Next, factor 1615, which is odd and ends in 5, making it divisible by 5.
- 1615 ÷ 5 = 323
- Factor 323: It can be divided by 17.
- 323 ÷ 17 = 19
- Thus, the prime factorization of 4845 is: 3 × 5 × 17 × 19.
List of Factors
Using the prime factorization, we can derive the factors of 4845:
- 1 (as every number is divisible by 1)
- 3
- 5
- 15 (3 × 5)
- 17
- 19
- 51 (3 × 17)
- 95 (5 × 19)
- 285 (15 × 19)
- 323 (17 × 19)
- 1615 (5 × 17 × 19)
- 4845 (the number itself)
Conclusion
The factors of 4845 include all the listed numbers, and understanding divisibility helps in various mathematical applications, including solving equations and simplifying fractions.