+0  
 
0
10
3
avatar+16 

Find a six-digit multiple of 64 that consists only of the digits 1 and 2.

how do you do this? the lcm can only be 1 and 64 but how does that help?

 Oct 28, 2023
 #1
avatar+1199 
-1

We know that a number is a multiple of 64 if it is a multiple of 4 and 16. A number is a multiple of 4 if the last two digits are a multiple of 4, and a number is a multiple of 16 if the last four digits are a multiple of 16.

The only possible last two digits of a six-digit multiple of 64 that consists only of the digits 1 and 2 are 12 and 22. If the last two digits are 12, then the last four digits are 1212, which is not a multiple of 16. Therefore, the last two digits must be 22.

To make the last four digits a multiple of 16, we can add 11 to the last three digits. If the last three digits are 112, then the last four digits are 1122, which is a multiple of 16.

Therefore, the six-digit multiple of 64 that consists only of the digits 1 and 2 is111122​.

 Oct 28, 2023

4 Online Users

avatar
avatar