SOLUTION: A four-digit number abcd is called cool if a is divisible by 4, the two-digit number ab is divisible by 5, the three-digit number abc is divisible by 6 and abcd is divisible by 7.

Question 1178646: A four-digit number abcd is called cool if a is divisible by 4, the two-digit number ab is divisible by 5, the three-digit number abc is divisible by 6 and abcd is divisible by 7. How many cool numbers are there where 8 is not one of the digits?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Our purpose at this forum is not to do your work for you; it is to help YOU learn how to do it.

There is no fancy mathematics involved in solving this problem. Do it yourself.

(1) a is divisible by 4. What are the possible values of a?
(2) ab is divisible by 5, so a is either 0 or 5. From (1) and (2), what are the possibilities for the string ab?
(3) abc is divisible by 6. For each of the possible strings ab, what digit(s) c make abc divisible by 6?
(4) For the possible strings abc from steps (1) to (3), what digit(s) make abcd divisible by 7?

RELATED QUESTIONS
What is a five-digit number divisible by both 2 and 5? What is a three digit number... (answered by funmath)

Let a and b be digits of a three �digit number �6ab� that is greater than 600. if... (answered by Edwin McCravy)

A three-digit number divisible by 5 has a hundreds digit that is 2 more than the tens... (answered by ankor@dixie-net.com)

A three- digit number divisible by 5 has a hundreds digit that is 2 more than the tens... (answered by richwmiller,MathTherapy)

what is the largest 5 digit number divisible by... (answered by Edwin McCravy)

find a number that; The last digit is even Sum of the digits is divisible by 3 The... (answered by jim_thompson5910)

Show the difference between a four-digit number and its reverse is divisible by... (answered by Edwin McCravy)

if the sum of the digits of a 3 digit number is divisible by 9, prove that the 3 digit... (answered by ikleyn)

Find the value of the digit A if the 5-digit number 12A3B is divisible by both 4 and 9,... (answered by MathLover1)