What is the units digit of 248^20?

Vincen wrote:What is the units digit of 248^20?

A) 0
B) 2
C) 4
D) 6
E) 8

Look for a pattern

248^1 = 248
248^2 = (248)(248) = ---4 [aside: we need not determine the other digits. All we care about is the units digit]
248^3 = (248)(248^2) = (248)(---4) = ----2
248^4 = (248)(248^3) = (248)(---2) = ----6
248^5 = (248)(248^4) = (248)(---6) = ----8

NOTICE that we're back to where we started.
248^5 has units digit 8, and 248^1 has units digit 8
So, at this point, our pattern of units digits keep repeating 8, 4, 2, 6, 8, 4, 2, 6, 8,...
We say that we have a "cycle" of 4, which means the digits repeat every 4 powers.

So, we get:
248^1 = --8
248^2 = ---4
248^3 = ----2
248^4 = ----6
248^5 = ----8
248^6 = ---4
248^7 = ----2
248^8 = ----6
248^9 = ----8
248^10 = ----4
etc.

Notice that when the exponent is a MULTIPLE of 4 (4, 8, 12, 16, ...), the units digit will be 6
Since 20 is a MULTIPLE of 4, we know that the units digit of 248^20 will be 6
Answer: D

Here's an article I wrote on this topic (with additional practice questions): https://www.gmatprepnow.com/articles/un ... big-powers

Cheers,
Brent

mbouayad14 wrote:20 is a multiple of 2....so why couldnt rhe answer be 4???

That would be true if it were the case that ALL exponents that are multiples of 2 yielded units digit 4

Cheers,
Brent

Vincen wrote: How can I find the units digit without making the whole calculus?

You should never try to calculate the actual value when asked for a units digit! It's all about finding the PATTERNS in the units digits. Try to find the patterns in these examples:
https://www.beatthegmat.com/if-r-s-and-t ... tml#548713
https://www.beatthegmat.com/if-n-and-m-a ... tml#544266
https://www.beatthegmat.com/what-is-the- ... tml#554073
https://www.beatthegmat.com/what-is-the- ... tml#544267
https://www.beatthegmat.com/what-is-the- ... tml#554073