What is the units digit of 18^47 ?

BTGmoderatorDC wrote:What is the units digit of 18^47 ?

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

OA B

Source: Magoosh

The units digit of 18^47 is the same as the units digit of 8^47.

Power cycle of 8:

8^1 = 8;
8^2 = ...4;
8^3 = ...2;
8^4 = ...6;

8^5 = ...8;
8^6 = ...4;
8^7 = ...2;
8^8 = ...6;

So the units digit of 8 in power cycle repeats a pattern of 4 numbers: 8, 4, 2, and 6

We have 18^47 = 18^(4*11 + 3)

Thus, the units digit of 18^47 would be the same as the units digit of 8^3 (ignoring 11 cycles of 4), which is 2.

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote:What is the units digit of 18^47 ?

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

OA B

Source: Magoosh

Since we care only about units digits, the units digit of 18^47 will be the same as the units digit of 8^47.

Let’s determine the units digit of 8^47 by determining the pattern of the units digits of 8^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 8. When writing out the pattern, notice that we are concerned ONLY with the units digit of 8 raised to each power.

8^1 = 8

8^2 = 4

8^3 = 2

8^4 = 6

8^5 = 8

The pattern of the units digit of powers of 8 repeats every 4 exponents. The pattern is 8–4–2–6. In this pattern, all positive exponents that are multiples of 4 will produce a 6 as their units digits. Thus:

8^48 has a units digit of 6.

8^47 has a units digit of 2.

Answer: B