Find the largest four digit number which has a total of exactly 3 factors. Assuming that 1 and the number itself are factors
you want the largest perfect square less than 10000. The three factors will be 1,√n, and n
Any number not a perfect square will have 4 or more factors (or just 2 factors if it is prime)
The largest prime less than 100 is 97 so the largest four digit number with 3 factors is 97^2=9409.
To find the largest four-digit number that has a total of exactly 3 factors, we need to understand factorization.
A number has a factor pair for each pair of numbers that multiply together to give the original number. For example, the number 12 has the factor pairs (1, 12), (2, 6), and (3, 4). A prime number only has two factors, since it can only be divided evenly by 1 and itself.
To have exactly 3 factors, the number must be a square number. This is because for a number to have an odd number of factors, it needs to be a perfect square.
The largest four-digit square number is 99^2, which is equal to 9801. However, this number has more than 3 factors. So, we need to look for the largest four-digit square number with exactly 3 factors.
The only possibility is a prime number squared. The largest four-digit prime number is 997. Therefore, the largest four-digit square number with exactly 3 factors is 997^2.
To calculate 997^2:
997^2 = 997 * 997 = 994009
Hence, the largest four-digit number with exactly 3 factors is 994009.
To find the largest four-digit number with exactly three factors, we need to find a number that has exactly two prime factors. This is because the total number of factors of a number is equal to the product of the exponents of its prime factorization plus one.
Let's start by considering the prime numbers. The first prime number is 2, followed by 3, 5, 7, 11, 13, and so on.
We need to find a number with exactly two prime factors. Since we want to find the largest four-digit number, we'll start with the largest prime numbers.
The largest four-digit number is 9999. We can divide it by the largest prime number, which is 997, to see if it is a factor. We use long division or a calculator to check if 9999 is divisible by 997. If it is not divisible, we move on to the next largest prime number.
If we divide 9999 by 997, the quotient is 10.06 (approximately). Since the quotient is not a whole number, 997 is not a factor of 9999.
We move on to the next largest prime number, which is 991. We divide 9999 by 991. If it is divisible, we continue dividing to see if it has any other prime factor. If it is not divisible, we move on to the next largest prime number.
If we divide 9999 by 991, the quotient is approximately 10.08. Again, since the quotient is not a whole number, 991 is not a factor of 9999.
We repeat this process with the remaining prime numbers until we find a four-digit number with exactly two prime factors.
Upon checking all prime numbers up to the square root of 9999, which is approximately 99, we find that none of them are factors of 9999.
Therefore, there is no four-digit number with exactly two prime factors.