Greatest 4-Digit Number
The greatest 4-digit number is 9999. It is the largest number that can be represented using four digits in decimal notation.
Prime Factorization of 9999
To express 9999 in terms of its prime factors, we will divide it by the smallest prime numbers until we reach 1.
Step-by-Step Prime Factorization
- Dividing by 3:
9999 is divisible by 3, since the sum of its digits (9 + 9 + 9 + 9 = 36) is divisible by 3.
9999 ÷ 3 = 3333
- Dividing by 3 again:
3333 is also divisible by 3.
3333 ÷ 3 = 1111
- Dividing 1111 by 11:
The next step is to check 1111 for divisibility by primes.
1111 is divisible by 11 (1111 ÷ 11 = 101).
- 101 is a prime number:
The final quotient, 101, is itself a prime number, meaning it cannot be divided further by any other prime.
Final Prime Factorization
Thus, the prime factorization of 9999 can be expressed as:
- 9999 = 3 × 3 × 11 × 101
- This can also be written as:
- 9999 = 3^2 × 11 × 101
In conclusion, the prime factors of the greatest 4-digit number, 9999, are 3 (squared), 11, and 101. This breakdown provides insight into the composition of this significant number.