Find the three digit number that satisfies the following conditions:
. Has a factor of 3.
. Has a factor of 5.
. Has a factor of 7.
. All digits are prime.
Describe the thinking process you went through to solve this problem.
3 * 5 * 7 = ?
I forgot that 0 is not prime.
However, 525 meets the criteria
735 also works.
so does 315
To find the three-digit number that satisfies the given conditions, we need to follow a systematic approach. Here's the step-by-step thinking process:
1. Identify the prime numbers: First, we need to identify the prime numbers less than 10, which are 2, 3, 5, and 7. These will be the possible digits in our three-digit number.
2. Identify the factors: Now, we know that our number must have factors of 3, 5, and 7. These can be obtained by multiplying any combination of the prime digits from step 1. Let's consider all the possibilities:
a. Take a digit 3 or 5 or 7 as the first digit. This digit will ensure that the number has a factor of 3, 5, or 7.
b. Take another digit from the remaining prime digits as the second digit. At this point, we will have two digits in our three-digit number.
c. Finally, take the remaining digit as the third digit. This will complete our three-digit number.
3. Form the numbers: Now, using all the combinations identified in step 2, we can create the possible three-digit numbers. This will give us a list of candidate numbers that satisfy the given conditions.
4. Check for the correct answer: From the list of candidate numbers, verify which satisfies all the conditions given in the problem. The correct three-digit number should have factors of 3, 5, and 7, along with all digits being prime.
Following this thinking process, we can find the three-digit number that meets all the conditions.