ziyuenlau wrote:
mcelroytutoring wrote:
Easy explanation:
\(2^{20}=4^{10}=16^5\)
All powers of 6 end with a 6 in the units digit, so \(16^5\) must also end with a 6. Thus, when divided by 10, the remainder must be 6.
mcelroytutoring Could you briefly explain this? I am not understand about this.
Sure! When you multiply 20 2s together, you get 10 4s because each pair of 2s makes a 4. (2 x 2 = 4) When you multiply 10 4s together, you get 5 16s because every pair of 4s makes a 16 (4 x 4 = 16).
Every power of 6 ends with a 6 because \((6)(6) =36\) and \((6)(6)(6) = (36)(6) = 216\) and \((6)(6)(6)(6) = 1296\), etc. And the remainder when you divide by 10 will always be equal to 6, because multiples of 10 always end in 0. \(36/10 = 3 R 6, 216/10 = 21 R 6, 1296/10 = 129 R 6\), etc.
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My name is Brian McElroy, founder of McElroy Tutoring (https://www.mcelroytutoring.com). I'm a 42 year-old Providence, RI native, and I live with my wife, our three daughters, and our two dogs in beautiful Colorado Springs, Colorado. Ever since graduating from Harvard with honors in the spring of 2002, I’ve worked as a private tutor, essay editor, author, and admissions consultant.
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