A) How many of the three digit numbers can be made from all of the digits, 1,3 and 7, and used only one each,are prime?
B) What about 2,3 and 4?
Once I get to know what the answer to the first one is, I'll figure out the second one myself.And then if I tell you what I got for the second part (b), can you please tell me if it's correct then?
number of digits
= 3x2x1
= 6 , we could actually list them
137
173
317
371
713
731
Here is a list of primes:
http://primos.mat.br/indexen.html
you will find that all are prime except
371, 713 and 731
731 =17 x 43
713 = 23 x 31
371 = 7 x 53
1+1=11
A) To find out how many three-digit numbers can be made using the digits 1, 3, and 7, and where each digit is used only once, we can follow these steps:
1. Start by listing the possible combinations of the three digits. In this case, we have 1, 3, and 7. So the possible combinations are:
- 137
- 173
- 317
- 371
- 713
- 731
2. Check each of these combinations to see if they are prime numbers. A prime number is a number that is only divisible by 1 and itself.
- 137: This is a prime number because it is only divisible by 1 and 137.
- 173: This is a prime number because it is only divisible by 1 and 173.
- 317: This is a prime number because it is only divisible by 1 and 317.
- 371: This is not a prime number because it is divisible by 7 and 53.
- 713: This is a prime number because it is only divisible by 1 and 713.
- 731: This is a prime number because it is only divisible by 1 and 731.
3. Count the number of prime numbers in the list. In this case, we have 4 prime numbers: 137, 173, 317, and 731.
Therefore, there are four prime three-digit numbers that can be made using the digits 1, 3, and 7, where each digit is used only once.
B) Now, let's consider the digits 2, 3, and 4. Following the same steps as before:
1. List the possible combinations of the three digits:
- 234
- 243
- 324
- 342
- 423
- 432
2. Check each combination for prime numbers:
- 234: This is not a prime number because it is divisible by 2, 3, and 13.
- 243: This is not a prime number because it is divisible by 3 and 81.
- 324: This is not a prime number because it is divisible by 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.
- 342: This is not a prime number because it is divisible by 2, 3, and 57.
- 423: This is not a prime number because it is divisible by 3 and 141.
- 432: This is not a prime number because it is divisible by 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, and 432.
3. There are no prime numbers in this case.
Therefore, there are no prime three-digit numbers that can be made using the digits 2, 3, and 4, where each digit is used only once.
Once you figure out the second part (B), feel free to let me know your answer, and I'll be happy to confirm if it's correct or provide any additional explanations.