Question
Download Solution PDFWhat is the digit in the units place of the number 12568^152?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The number is 12568152.
Formula used:
The last digit of a power depends on the cyclicity of the last digit of the base number.
Calculations:
The last digit of 12568 is 8.
The cyclicity of 8 is as follows:
81 = 8 (Last digit = 8)
82 = 64 (Last digit = 4)
83 = 512 (Last digit = 2)
84 = 4096 (Last digit = 6)
After 84, the last digits repeat in the cycle: 8, 4, 2, 6.
To find the position of 8152 in the cycle:
⇒ 152 ÷ 4 = 38 remainder 0
A remainder of 0 means we take the last digit of 84, which is 6.
The digit in the units place of 12568152 is 6.
The correct answer is option (1).
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