I am a prime number between 40 and 50. If you add one to me the sum of the prime factors of that composite number is 11. What number a I.
If the prime factors are 6 and 7 of the prime number plus 1.....
It's impossible.
To solve this problem, let's list down the prime numbers between 40 and 50:
41, 43, 47
Now, let's check each of these prime numbers by adding one to them and finding the prime factors of the resulting composite number:
For 41 + 1 = 42, the prime factors are 2, 3, and 7, which sum up to 12.
For 43 + 1 = 44, the prime factors are 2 and 11, which sum up to 13.
For 47 + 1 = 48, the prime factors are 2, 2, 2, 2, and 3, which sum up to 11.
From the above analysis, we can see that the prime number between 40 and 50 that satisfies the condition is 47.
To find the prime number you are given the clues about, we can follow a step-by-step approach:
Step 1: Find the composite number by adding one to the given prime number.
Let's assume the prime number between 40 and 50 is represented by 'x.' Adding one to 'x' gives us 'x + 1.'
Step 2: Determine the prime factors of the composite number (x + 1).
To find the prime factors of (x + 1), we need to factorize it. Prime factorization means expressing the number as a product of prime numbers.
Step 3: Calculate the sum of the prime factors.
After factorizing (x + 1) into its prime factors, calculate their sum.
Step 4: Identify the composite number with a total sum of prime factors equal to 11.
Among the possible values of x within the given range, check for the composite number whose sum of prime factors is equal to 11.
Let's apply these steps to find the answer:
Step 1: Since you are a prime number, we have a range from 41 to 49, inclusive.
Step 2: Let's take each number from this range and add one to it:
41 + 1 = 42 (2 * 3 * 7)
42 + 1 = 43 (prime number)
43 + 1 = 44 (2 * 2 * 11)
44 + 1 = 45 (3 * 3 * 5)
45 + 1 = 46 (2 * 23)
46 + 1 = 47 (prime number)
47 + 1 = 48 (2 * 2 * 2 * 2 * 3)
48 + 1 = 49 (7 * 7)
Step 3: Now, let's calculate the sum of the prime factors for each composite number:
42: 2 + 3 + 7 = 12
44: 2 + 2 + 11 = 15
45: 3 + 3 + 5 = 11
46: 2 + 23 = 25
48: 2 + 2 + 2 + 2 + 3 = 11
49: 7 + 7 = 14
Step 4: Since you mentioned that the sum of the prime factors should be 11, we find that the composite number 45 (3 * 3 * 5) has the desired sum.
Therefore, the prime number you are is 45 - 1 = 44.
So, you are the prime number 44, as described.