# number theory

Write the numbers 25, 32, 56 to the base 5.

write 47, 68, 127 to the base 2.

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#### Solution Preview

Base 5:

25:

25= 5*5+0 ---> Keep 0 Take 5 to the next step:

5= 5*1+0 ---> keep 0 and 1 is also less than 5 so keep that too.

Now put the numbers beside each other: 1 then 0 then 0:

(25) in base 5= 100. Verify that 1*5^2+0*5+0=25

32:

32= 5*6+2 ---> keep 2 and take 6 to the next step:

6= 5*1+ 1 ---> keep 1 and 1 is also less than 5 so keep that too.

Now put the numbers beside each other: 1 then 1 then 2:

(32) in base 5= 112. Verify that 1*5^2+1*5+2=32

56:

56= 5*11+1 ---> keep 1 and take 11 to the next step:

11= 5*2+ 1 ---> ...

#### Solution Summary

This solution is comprised of a detailed explanation to write the numbers 25, 32, 56 to the base 5 and 47, 68, 127 to the base 2.

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