Numbers and

Question

^{If x is a positive integer what is the units digit of} (24)^5+2x (36)⁶ (17)^3?

Answer 1

First let's split first exponential into two parts, 24⁵ times 24^2x.

 

Factor 24⁵ has units digit 4; factor 36⁶ has units digit 6; factor 17³ has units digit 3;

 

factor 24^2x has units digit 6...if x=1, units digit 6 if x = 2, 6 if x = 3, etc.

 

(24)^5+2x (36)⁶ (17)³ is the question (the question mark in the title should not be part of an exponent).

 

The final answer's units digit is therefore controlled by this units-digits product:  (4•6)•6•3, in order.  It's TWO.

 

 

 

Answer 2

I pretty sure the One's place digit will be a 2, but I'd sure like another opinion.

 

The last digit of the final product will result from the final digit of the individual factors involved.  These are driven by the final digit of the numbers shown: 4 in the 24; 6 in the 36; and 7 in the 17.  

 

So we just need to determine what the final digit is of the last two: 

(6^6)(7^3) will drive the final digit to be an 8 [and still show up on a normal scientific calculator].

 

Taking a look at what the first three possible factors for the term with the variable shows that these all end in a 4.

 

So the final product of 8 and 4 will drive the last digit to be 2.  Anyone else care to chime in?

 

P.S. I meant to say "emerges" above : )