Find the largest four digit number which has a total of exactly 3 factors. Assuming that 1 and the number itself are factors

20 or 30

9409

To find the largest four-digit number with exactly 3 factors, we can start by understanding what it means to have exactly 3 factors.

In general, the factors of a number are the numbers that divide it evenly without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Note that 1 and the number itself are always factors.

For a number to have exactly 3 factors (including 1 and itself), it means that the number is a perfect square of a prime number. This is because a perfect square only has odd number of factors, and if we exclude 1 and the number itself, we are left with exactly 1 additional factor.

To find the largest four-digit number that is a perfect square of a prime number, we can start from the largest four-digit number (9999) and work backwards. We can check if each number is a perfect square by finding its square root and checking if it is a whole number or an integer.

Let's go through the process step by step:

Step 1: Start with the largest four-digit number, 9999.

Step 2: Find the square root of 9999. It is approximately 99.994.

Step 3: Check if the square root is a whole number. In this case, it is not.

Step 4: Move to the next largest four-digit number, which is 9998.

Step 5: Find the square root of 9998. It is approximately 99.989.

Step 6: Check if the square root is a whole number. In this case, it is not.

Step 7: Repeat steps 4-6 until we find a number whose square root is a whole number.

Step 8: The largest four-digit number that is a perfect square of a prime number is the number we found in step 7.

Following this process, we can continue checking the square roots of smaller numbers until we find the largest four-digit number that is a perfect square of a prime number.