What is my number?
Clue 1. My number is a multiple of 5 and is less than 50.
Clue 2. My number is a multiple of 3.
Clue 3. My number has exactly 8 factors.
5, 10, 15, 20, 25, 30, 35, 40, 45
Which of those is divisible by 3?
Which of those has exactly 8 factors?
To find your number, we need to look for a number that satisfies all the given clues. Let's break down each clue and apply it to identify the possible numbers.
Clue 1 states that your number is a multiple of 5 and is less than 50. So, we can list the numbers 5, 10, 15, 20, 25, 30, 35, 40, and 45 as possible candidates.
Clue 2 states that your number is a multiple of 3. Looking at our list, we can see that the numbers 15, 30, and 45 satisfy this condition.
Now, let's move on to Clue 3, which states that your number has exactly 8 factors. Factors are the numbers that divide evenly into another number without leaving a remainder. In this case, we need to find the numbers from our list that have eight factors.
To determine the number of factors, we can prime factorize each number and use the formula: (power of prime factors + 1) * (power of next prime factor + 1) * ...
For 15, the prime factorization is 3 * 5. Applying the formula: (1+1) * (1+1) = 4 factors, so 15 does not have exactly 8 factors.
For 30, the prime factorization is 2 * 3 * 5. Applying the formula: (1+1) * (1+1) * (1+1) = 8 factors, so 30 satisfies the condition.
For 45, the prime factorization is 3 * 3 * 5. Applying the formula: (2+1) * (1+1) * (1+1) = 12 factors, so 45 does not have exactly 8 factors.
Based on the given clues, we can conclude that the only number that satisfies all the conditions is 30. Therefore, your number is 30.