# How many six-digit positive integers are there, which is evenly divisible by 4 or 9?

• Feb 2nd 2010, 09:35 AM
Monika1987
How many six-digit positive integers are there, which is evenly divisible by 4 or 9?
How many six-digit positive integers are there, which is evenly divisible by 4 or 9?

(If you let A be the amount of six-digit positive integers that are evenly divisible by 4 and B be the amount of six-digit positive integers that are evenly divisible by 9, so you should therefore
determine the number of elements in A ∪ B.
Remember that A and B in this case may not be disjoint sets.)

/Monica(Clapping)
• Feb 2nd 2010, 11:00 AM
HallsofIvy
Quote:

Originally Posted by Monika1987
How many six-digit positive integers are there, which is evenly divisible by 4 or 9?

(If you let A be the amount of six-digit positive integers that are evenly divisible by 4 and B be the amount of six-digit positive integers that are evenly divisible by 9, so you should therefore
determine the number of elements in A ∪ B.
Remember that A and B in this case may not be disjoint sets.)

/Monica(Clapping)

How many such numbers are divisible by 4? How many such numbers are divisible by 9? How many such numbers are divisible by 4*9= 36?

Are we to assume that by "six-digit positive numbers" you mean numbers from 100000 to 999999?
• Feb 3rd 2010, 02:34 AM
Monika1987
yes. By six-digit number they want to know from 100000-999999 how many numbers there are that is evenly divisible by 4 or 9.
example:
444444 and 999999 is such numbers. so how many between 100000-999999?
• Feb 3rd 2010, 09:30 AM
Soroban
Hello, Monika1987!

Quote:

How many 6x-digit positive integers are there that are evenly divisible by 4 or 9?
There are 900,000 six-digit numbers.

Every 4th number is divisible by 4: .$\displaystyle \frac{900,\!000}{4} \:=\:225,\!000$ numvbers divisible by 4.

Every 9th number is divisible by 9: .$\displaystyle \frac{900,\!000}{9} \:=\:100,\!000$ numbers divisible by 9.

But every 36th number is divisible by both 4 and 9: .$\displaystyle \frac{900,\!000}{36} \:=\:25,\!000$

$\displaystyle \text{Therefore: }\;225,\!000 + 100\!,000 - 25,\!000 \;=\;\boxed{300,\!000}\,\text{ numbers divisible by 4 or 9.}$