A mathematician is studying the powers of 7 and their unit digits. What is the unit digit of 74008.
(a) 7
(b) 9
(c) 3
(d) 1

Question

A mathematician is studying the powers of 7 and their unit digits. What is the unit digit of 74008.
(a) 7
(b) 9
(c) 3
(d) 1

ONLiNE UPSC · Accepted Answer

To find the unit digit of 74008
Let&rsquo;s calculate the first few powers of 7 and their unit digits:
71 = 7 (unit digit = 7)
72 = 49 (unit digit = 9)
73 = 343 (unit digit = 3)
74 = 2401 (unit digit = 1)
Now, we see that the unit digits repeat every 4 terms:
7, 9, 3, 1
4008 &divide; 4 = 1002 remainder 0,
We are looking for the unit digit of 74, which is the same as the unit digit of 70 in the repeating cycle.
We know the unit digit of 74 is 1, so the unit digit of 74008 is also 1.

Hence, option d is correct.

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A mathematician is studying the powers of 7 and their unit digits. What is the unit digit of 74008. (a) 7 (b) 9 (c) 3 (d) 1