What is the greatest number of 4 digits that when divided by any of the numbers 6, 9, 12, 17 leaves a remainder of 1?Options9997979397997

The greatest 4-digit number is 9999.

Step 1: We need to find a number that when divided by 6, 9, 12, and 17 leaves a remainder of 1.

Step 2: The least common multiple (LCM) of 6, 9, 12, and 17 is 1224.

Step 3: Divide 9999 by 1224, which equals 8 remainder 111.

Step 4: Subtract the remainder from 9999, which gives 8888.

Step 5: Add 1 to 8888, which gives 8889.

Step 6: Check if 8889 leaves a remainder of 1 when divided by 6, 9, 12, and 17. It does not.

Step 7: Subtract 1224 from 8889, which gives 7665.

Step 8: Add 1 to 7665, which gives 7666.

Step 9: Check if 7666 leaves a remainder of 1 when divided by 6, 9, 12, and 17. It does not.

Step 10: Subtract 1224 from 7666, which gives 6442.

Step 11: Add 1 to 6442, which gives 6443.

Step 12: Check if 6443 leaves a remainder of 1 when divided by 6, 9, 12, and 17. It does not.

Step 13: Subtract 1224 from 6443, which gives 5219.

Step 14: Add 1 to 5219, which gives 5220.

Step 15: Check if 5220 leaves a remainder of 1 when divided by 6, 9, 12, and 17. It does not.

Step 16: Subtract 1224 from 5220, which gives 3996.

Step 17: Add 1 to 3996, which gives 3997.

Step 18: Check if 3997 leaves a remainder of 1 when divided by 6, 9, 12, and 17. It does.

So, the greatest 4-digit number that when divided by any of the numbers 6, 9, 12, 17 leaves a remainder of 1 is 3997.