1)List all #s less than 100 with exactly 5 factors.
For this I got 16 , 64, and 81.
2)Find the next 2 #s, each greater than 100, that have exactly 5 factors.
This is the problem I am having trouble with.
2*2*2*2=16, which is only 4 factors. The factors do not include 1. 32 would have 5 factors. 64 has 6, and 81 has 4. You need to be aware that the factors don not need to be the same numerical value. For example, 2*2*2*2*3= 48.
I hope this helps. Thanks for asking.
To find the next two numbers, each greater than 100, that have exactly 5 factors, we can use the concept of prime factorization.
First, let's understand what it means for a number to have exactly 5 factors. When a number has exactly 5 factors, it means that it is a perfect square of a prime number.
Now, let's follow a step-by-step approach to find the next two numbers:
1) Start with finding the square root of the largest number greater than 100. In this case, the largest number is 101, and its square root is approximately 10.05. We will consider the next whole number, which is 11.
2) Prime factorize the number 11. Since it is a prime number itself, its prime factorization is simply 11.
3) Square the prime factors obtained. In this case, 11 squared is 121.
So, the next number greater than 100 with exactly 5 factors is 121.
Now, let's repeat the process to find the next number:
1) Find the square root of the last number we obtained, which is 121. The square root of 121 is 11.
2) Prime factorize 11. As mentioned earlier, since it is a prime number itself, its prime factorization is simply 11.
3) Square the prime factors obtained. In this case, 11 squared is 121.
So, the second number greater than 100 with exactly 5 factors is 121 again.
Hence, the next two numbers each greater than 100, that have exactly 5 factors, are 121 and 121.