What is the smallest integer that is greater than zero that has only zeros and ones is divisible by 225?

pinkroses3709 - 2007-10-14 21:11:54 - Mathematics

Best Answer:

Lets see, just keep adding it up: 225, 450, 675, 900, 1125, 1350, 1575, 1800, 2025, 2250, 2475, 2700, 2925, 3150, 3375, 3600, 3825, dude your teacher sucks, 4050, 4225, 4450, 4675, 4900, 9800, 10025, 80400, 90625, 95525, 99575, 99800, 100025, SCREW THIS. Good luck.

Answer:

Lets see, just keep adding it up: 225, 450, 675, 900, 1125, 1350, 1575, 1800, 2025, 2250, 2475, 2700, 2925, 3150, 3375, 3600, 3825, dude your teacher sucks, 4050, 4225, 4450, 4675, 4900, 9800, 10025, 80400, 90625, 95525, 99575, 99800, 100025, SCREW THIS. Good luck.

225 = 9 x 25 anything that has 2 zeros at the end will be divisible by 25 then for it to be divisible by nine u have the sum of the digits should be divisible by 9 and since u have to have only 1's and 0's the number would have 9 1's and 2 0's at the end so the number would be 11,111,111,100

The first number to consider is: 11111111100. 225 is divisible by 9. There is a rule that numbers divisible by 9 have digits that add up to a multiple of 9. Also, the number must end in 00 to be divisible by 25 and only contain 1s and 0s. This number is indeed divisible by 225.