find the greatest four-digit number that has exactly three positive factors.
not sure about the question but maybe
9990
1 and 9990
5 and 1998
10 and 999
sorry if this was the wrong idea
To find the greatest four-digit number that has exactly three positive factors, we need to understand what a positive factor is. A positive factor of a number is a number that divides the original number without leaving a remainder.
We know that the factors of any number are pairs of numbers that when multiplied together, give the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
To determine the number of factors a number has, we need to understand its prime factorization. Prime factorization is the process of expressing a composite number as a product of its prime factors. Let's go step by step:
1. Start with the smallest prime number, which is 2.
2. Check if the number is divisible by 2. Find the quotient of division and reduce the number.
3. Continue dividing the reduced number by prime numbers until the reduced number becomes 1.
Let's apply this process to find a four-digit number with exactly three factors:
The lowest four-digit number is 1000.
Prime factorize 1000: 1000 = 2^3 * 5^3
Since we need exactly three factors, we can consider numbers in the form of p^2 * q, where p and q are prime numbers. In this case, p and q can only be 2 or 5.
Let's consider all possible combinations:
1. p=2, q=5: (2^2) * (5) = 20. However, 20 is not a four-digit number.
2. p=5, q=2: (5^2) * (2) = 50. But 50 is also not a four-digit number.
We see that there is no combination of prime factors that will yield a four-digit number with exactly three factors. Therefore, there is no greatest four-digit number that has exactly three positive factors.