Question

11. Find the last two digits of 2^20
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Answer 1

Answer:

What are the last two digits of 2^20 ,without using calculator? So we get 2–4–8–6 repeated forever. 20th element of that cycle is 6. 76 is the last two digits.

Last 2 digits of N ≡ Rem(N÷100)

2^20

=(2^10)²

=1024²

=(100×10+24)²

≡24² MOD 100

=576 mod100

≡ 76 mod100

∴last two digits of 2^20 is 76

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