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Topic: Remainder math homework
June 15, 2019 / By Jordie
Question: Hello, I'm doing math homework right now and i have stumbled on to this problem: What is the last digit of 2*85 (2 to the 85th power). Please help me, and explanations would be very much appreciated. Thank You. yes, it's actually honors, but we're only starting it because school started yesterday.

Hanael | 10 days ago
base 2 follows a pattern 2^1=2 2^2=4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 as you can see the last digit alternates in the pattern 2,4,8,6,2,4,8,6 forever. this pattern is a repeating unit of 4 digits in length so you see how many lots of 4 go evenly into 85. the answer is 21 lots although this part is unimportant. the remainder is 1 so the 85th power will have the same last digit as the first character.i.e the last digit will be a 2 hope that helped
👍 148 | 👎 10

We found more questions related to the topic: Remainder math homework

base 2 follows a pattern 2^1=2 2^2=4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 as you can see the last digit alternates in the pattern 2,4,8,6,2,4,8,6 forever. this pattern is a repeating unit of 4 digits in length so you see how many lots of 4 go evenly into 85. the answer is 21 lots although this part is unimportant. the remainder is 1 so the 85th power will have the same last digit as the first character.i.e the last digit will be a 2 hope that helped

Edgar
You should use (shift + 6) for power of: 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 The pattern is 2, 4, 8, 6, 2, 4, 8, 6 etc... On 2^84, the last digit is 6 because the it is a multiple of 4 which means it's the last one in the pattern. That means the next one must be 2 because the pattern starts over so 2^85 ends in 2.
👍 50 | 👎 6

Calvin
powers of 2 (starting at 1) 2 , 4, 8 , 16, 32, 64, 128 , 256 .... Notice how the last digit cycles 2,4,8,6,2,4,8,6 ..... repeating after every 4th power. 2^85 = 2^(21*4 + 1) = 2^(21*4) * 2^1 2 raised to any power which is a multiple of 4 gives a number ending in 6. One more power of 2 then gives you something that ends in 2.
👍 41 | 👎 2

Alfrid
2^85 [^ indicates to the power] now 2^2=4 2^3=8 2^4=16 2^5=32 last digits are 4,8,6,2 2^6=64 2^7=128 2^8=256 2^9=512 last digits are 4,8,6,2 similarly every fourth power after 2^9 will have last digit as 2 i,e 2^13,2^17,2^21,2^25...2^49.... .....2^85 will have last digit as 2
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Tamsen
it relies upon at ur college. At my college I took Algebra a million in 9th grade yet then took Geometry over the summer season so now i'm taking Algebra 2 in tenth grade. At my college that's progressed.
👍 23 | 👎 -6

Richarda
Haha You go: 2 x 2 x 2 x 2 x .................2^85... There is no easy way lady! Sorry And this problem just can't be a ninth grade problem
👍 14 | 👎 -10