my math book tells me (Use the digits0,2,and5 to make a three digit numberthat has both 2 and 5 as factors.) please help
Which of these triple-digit numbers can be divided evenly by both 2 and 5?
205
250
502
520
250
520
To create a three-digit number that has both 2 and 5 as factors using the digits 0, 2, and 5, we need to arrange these digits in a way that ensures the number is divisible by both 2 and 5. Here's how we can do it step by step:
Step 1: We know that the number needs to have both 2 and 5 as factors. Therefore, the number must be divisible by 2 and end with 0 or 2, as these are the available digits.
Step 2: Since the number must be divisible by 5, it must end with 0 or 5. We already established that it should end with 0 or 2 to be divisible by 2, so the only possible options for the last digit are 0 or 2.
Step 3: Now, we need to determine the other two digits. We have used one of the digits (0 or 2) for the last digit. The remaining two digits are 2 and 5.
Step 4: To arrange these two digits in a way that the number is divisible by 2, they should be placed in such a way that the last digit is even. Therefore, we can't use 5 as the middle digit since it is an odd number. This leaves us with 2 as the middle digit.
Step 5: Putting everything together, the three-digit number that has both 2 and 5 as factors is 520.
To verify, you can check if the number 520 is divisible by both 2 and 5 using basic division.