Units Digit of 2^57Date: 10/07/2001 at 03:11:52 From: Lauren Wyluda Subject: 8th grade algebra What is the units digit of 2 to the power of 57? This would help me out tremendously. Thank you, Lauren Date: 10/07/2001 at 11:29:27 From: Doctor Paul Subject: Re: 8th grade algebra Look at the units digits of the following powers of 2: 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 2^9 = 512 2^10 = 1024 Do you see a pattern? The units digits cycle through the numbers 2, 4, 8, 6 and then start over again. So when n is a multiple of four, the units digit of 2^n is 6. When n is one more than a multiple of four, the units digit of 2^n is 2. When n is two more than a multiple of four, the units digit of 2^n is 4. When n is three more than a multiple of four, the units digit of 2^n is 8. Since 57 = 14*4 + 1 is one more than a multiple of four, it follows that the units digit of 2^57 is 2. In fact, 2^57 = 144115188075855872 and so the formula works. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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