Sure, let's solve the problem of finding the largest 6-digit number that is exactly divisible by 60 step-by-step.
1. Identify the largest 6-digit number:
The largest 6-digit number is 999,999.
2. Check divisibility conditions:
For a number to be divisible by 60, it must be divisible by 2, 3, and 5.
3. Divisibility by 2:
A number is divisible by 2 if it is even. Since 999,999 is an odd number, it is not divisible by 2. Therefore, the largest 6-digit even number is 999,998.
4. Divisibility by 60 (including 2, 3, and 5):
- Divisibility by 2: We've made our number even, so it's divisible by 2.
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For practical purposes, since most large even numbers divisible by 60 also need to be verified for divisibility by 3.
- Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5. Since we're working with even numbers (ensuring divisibility by 2), let's adjust the last digit to 0, making it divisible by both 2 and 5 automatically.
5. Finding largest divisible number by 60:
Now, starting from 999,998 (adjusting to nearest number ending in 0 we get 999,990), let's decrease by steps of 2 until we find a number that meets all the criteria:
- Test if 999,990 is divisible by 3, and then by 60.
By performing these tests and continuing the process, you would determine that the largest 6-digit number that is divisible by 60 is 999,960.
