Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of?
Is it 16?
To find the number that Eduardo is thinking of, we need to understand the concept of factors. Factors are numbers that can be divided evenly into another number.
For a number to have exactly 5 factors, it must be a prime number raised to the power of 4 (p^4), where p is a prime number. This is because the factors of a number in the form p^4 are 1, p, p^2, p^3, and the number itself.
So, let's identify the prime numbers between 1 and 20:
2, 3, 5, 7, 11, 13, 17, and 19.
Now, we need to check if any of these prime numbers raised to the power of 4 fall within the range of 1 to 20.
Calculating the powers of the prime numbers, we have:
2^4 = 16
3^4 = 81 (which is outside our range)
5^4 = 625 (also outside our range)
7^4 = 2401 (outside the range)
11^4, 13^4, 17^4, and 19^4 are all greater than 20.
Therefore, from our calculations, we can conclude that there is no number between 1 and 20 that has exactly 5 factors. Eduardo might be mistaken in his thinking, or he's not considering numbers within the given range.