Question

The 6-digit number 789ABC is divisible by 7, 8, and 9, and all of its digits are distinct. What is the 3-digit number ABC?

Answer 1

ABC = 264.

Explanation:

The number is divisible by 7*8*9 = 504.

504 * 1500 = 756000

Lets try a larger value:

`504 * 1580

= 796320

So we are close to the number required and the multiplier must be less than 1580.

504 * 1570 = 791280

504 * 1567 = 789768

We are close - the first 3 numbers are correct but it's not this one as some of last 3 digits are duplicated.

504 * 1566 = 789264 - That's the one

Answer 2

264

Explanation:

This is the answer because:

1) You have to know the divisibility rules of 7, 8, and 9:

• Divisibility rule of 7: The digit in the units place of a number should be multiplied by 2, and then the product needs to be subtracted from the original number.
• Divisibility rule of 8: The last three digits of a number have to be divisible by 8.
• Divisibility rule of 9: The digits have to add up to a multiple of 9.

2) Since 7+8+9 equals to 24, the last three digits have to add up to 24 to make 36 (divisible by 9).

3) The number also has to divisible by 7 and 8.

4) 264 adds up to 36 (the digits: 2,4, and 6), the number is divisible by 8, and finally, 789264 is divisible by 7.

Therefore, ABC = 264

Hope this helps! :)