A three digit number has the same hundreds, tens and units digit. The sum of the prime factors of the number is 47. What is the 3 digit number?
is 111 prime?
nope, 1,3, 37, 111
but 111 is certainly a factor of whatever our answer is
111*1 or 2 or 3 or whatever up to 9
so 3, 37 and what?
How about 7 ?
777 = 7 * 3 * 37
10+37 = 47 sure enough
what are the factors of 777?
7, 111
7,3,37
To find the three-digit number that satisfies the given conditions, we need to follow these steps:
1. Since the hundreds, tens, and units digit are the same, we can represent the number as 111x, where x is the common digit.
2. We know that the sum of the prime factors of the number is 47. Therefore, we need to find all the prime factors of 111x and check if their sum is 47.
3. Prime factorize 111x:
- The prime factorization of 111 can be written as 3 x 37.
- Since x is the common digit, it must be a prime factor as well.
4. Determine the possible values of x by considering its prime factors:
- The sum of the prime factors must be 47, so we need to find the values of x that satisfy 3 + 37 + x = 47.
- Solving this equation, we get x = 7.
5. Substitute the value of x back into the original expression to find the three-digit number:
- The number is 1117.
Therefore, the three-digit number that satisfies the given conditions is 1117.