A three digit number has the same hundreds, tens, and ones digits. The sum of the prime factors of the number is 47. What is the three digit number?

Question

This problem is regarding using the prime factorization of numbers.  Can get the right answer but need and explanation of how to begin this process and take it through till the end.

Answer 1

Hi Chrissie,

 

Since the three digits of the number are the same, you can look at it as 100x + 10x +x or 111x.

 

Now thinking about factorization, you know that "x" is a factor so what are factors of 111? Divide prime numbers between 2 and 9 into 111 since you are looking for prime factors.

 

3 and 37 work. No others do. 3 times 37 is 111.

 

So to solve the problem, you would  add x + 3 + 37 and set them equal to 47.  x therefore has to equal 7 and the three digit number is 777.

Answer 2

Its got to be 111 or 222 or 333 or 444 or 555 or 666 or 777 or 888 or 999.

 

Prime factor 111: 3 x 37. The sum of them is 40. So not 111

 

Prime factor 222: 2 x 3x 37. The sum of them is 42

 

Do the same for 333,444,555 etc

 

It turns out to be 777

7 x 3x 37. 

Answer 3

"A three digit number has the same hundreds, tens, and ones digits"     There are 9 possibilities:

  111  222  333  444  555  666  777  888  999

 

"The sum of the prime factors of the number is 47"   might possibly have one or more of these values added to form the sum:

   2  3  5  7  11  13  17  19  23   29   31   37   43      [note:  higher primes won't work]

 

One method is just to list the prime factors of each possibility and their sum:

 

                                             sum of

3-digit        prime                    prime

number      factors                  factors

111           3  37                        40
222           2   3  37                   42
333           3   3  37                   43
444           2   2   3  37              44
555           3   5  37                   45
666           2   3   3  37              45
777           3   7  37                   47
888           2   2   2  3  37          46
999           3   3   3   37             46

 

Now, simply pick the number with the sum of the prime factors equal to 47.