Question 1205180: What's the total of one, two, three-digit prime numbers that can be formed using the digits 2, 3, 5 and 7. No digit can be used more than once in a number.
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52817)   (Show Source):
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
The numbers 2,3,5, and 7 are prime since the only factors are 1 and themselves.
Make a 4x4 table listing the values 2,3,5,7 along the left and top like so
Cross out the northwest main diagonal. This is because we cannot re-use the same digit twice.
The remaining cells are filled in by concatenating the headers. I'll have the left header go first and then the top next.
| 2 | 3 | 5 | 7 | | 2 | X | 23 | 25 | 27 | | 3 | 32 | X | 35 | 37 | | 5 | 52 | 53 | X | 57 | | 7 | 72 | 73 | 75 | X |
The "2" column and "5" column can be crossed out because of the divisibility by 2 and divisibility by 5 rules.
27 is composite since 27 = 3*9
57 is composite since 57 = 3*19
Or you can use the divisibility by 3 rule to check 27 and 57 are multiples of 3.
Of that table, the primes are: 23, 37, 53, 73
Refer to a list of primes. Or you can check each one by one.
I'll let you handle the possible 3 digit primes that can be formed with 2,3,5,7.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
1-digit numbers....
2, 3, 5, and 7 are all prime numbers.
ANSWERS: 2, 3, 5, 7
2-digit numbers....
A 2-digit number is not prime if the last digit is 2 or 5, so the last digit has to be 3 or 7.
The possibilities are 23, 27, 53, and 57.
27 and 57 are not prime because their digit sum is divisible by 3.
23 and 53 are both prime, by inspection
ANSWERS: 23, 53
3-digit numbers....
Again the last digit can't be 2 or 5; it has to be 3 or 7.
The 3-digit combinations 2,3,7 and 3,5,7 won't work because the digit sum is divisible by 3.
The other 3-digit combinations are 2,3,5 and 2,5,7; in each of those combinations neither the 2 nor the 5 can be the last digit, so the possible prime numbers are 253, 523, 257, and 527.
Assuming we aren't working the problem simply by checking a list of prime numbers, here we have some actual detective work to do to see which if any of these are prime numbers.
I won't go into details (I leave that for the student); the prime numbers among these are 523 and 257.
ANSWERS: 257, 523
Final list of 1-, 2-, or 3-digit prime numbers using digits 2, 3, 5, and 7 without repetition:
2, 3, 5, 7, 23, 53, 257, 523
Since "total" is not a formal mathematical term, I won't guess what the expected answer is to the given problem. The student can use this list to answer the question, based on his/her interpretation.
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