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How to Solve: Last Two Digits of Power of 6

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How to Solve: Last Two Digits of Power of 6 [#permalink] New post   21 Sep 2024, 00:44
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How to Solve: Last Two Digits of Power of 6

Hi All,

I have posted a video on YouTube to discuss Last Two Digits of Power of 6



Attached pdf of this Article as SPOILER at the top! Happy learning!

Following is Covered in the Video
    • Theory of Last Two Digits of Power of 6
    • Find Units’ digit of 671 ?
    • Find Units’ digit of 612517 ?


Theory of Last Two Digits of Power of 6

• To find Last Two Digits of any positive integer power of 6


We need to find the cycle of last two digits of power of 6
61 last two digits is 06
62 last two digits is 06*6 = 36
63 last two digits is 36*6 = 16
64 last two digits is 16*6 = 96
65 last two digits is 96*6 = 76
66 last two digits is 76*6 = 56
67 last two digits is 56*6 = 36
68 last two digits is 36*6 = 16





=> The power repeats after every 5th power
=> Cycle of last two digits of power of 6 = 5 (ignoring 61)
=> We need to subtract one from the power and then divide the power by 5 and check the remainder
=> Last two digits will be same as last two digits of 61+Remainder

NOTE: If Remainder is 0 then last two digits = last two digits of 61+Cycle = last two digits of 66 = 56

Q1. Find Last two digits of 671?

Show: ::
Sol: We need to subtract 1 from 71 and then divided the remaining power (71-1=70) by 5 and get the remainder
70 divided by 5 gives 0 remainder = remainder of 5
=> Last two digits of 671 = Last two digits of 61+5 = 56


Q2. Find Last two digits of 612517?

Show: ::
Sol: 12517 - 1 = 12516
12516 divided by 5 will give the same remainder as 6 by 5 which is 1
Watch this video to Master Divisibility Rules
=> Last two digits of 612517 = Last two digits of 61+1 = 36


Hope it helps!

Link to Theory for Last Two digits of exponents here.

Link to Theory for Units' digit of exponents here.
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How to Solve: Last Two Digits of Power of 6 [#permalink]
21 Sep 2024, 00:44
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