Find the last digit of 3278 power 123
Weblast digit of 1273^122!= 3^122! Now. 3 follows a patter in terms of its powers and last digits: 3^1 = 3 3^2 = 9 3^3 = 27 3^4 = 81 3^5 = 243 therefore, the pattern repeats itself with last … WebThis problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Compute and justify your answer (guessing the pattern will not do): (a) The last digit of 65^35 . (b) 2^123 mod 15. (c) 6^65 mod 13. Compute and justify your answer (guessing the pattern will not do): (a) The ...
Find the last digit of 3278 power 123
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Webso the last digit of 7 100 is 1. Note that φ ( 100) = 100 ( 1 − 1 2) ( 1 − 1 5) = 40 using Euler's product formula, so since 3 and 100 are coprime, 3 φ ( 100) ≡ 3 40 ≡ 1 (mod 10) and so … WebSo when we are looking to find the ones digit of $7^{2011}$ we only need to pay attention to the ones digit in each successive power. Starting with the first power these are $7,9,3,1$ and then the sequence repeats. Since $$2011 = 502 \times 4 + 3$$ this means that for $7^{2011}$ we will go completely through this sequence of last digits 502 ...
WebDec 13, 2024 · In short, the last digit of these huge powers will be the same as that of a reduced power consisting of the first digit of the base (mod 10), raised to the last two digits of the exponent (mod 100). The units in a sequence of powers repeat in patterns of 4 at most, so we can use mod 4 to reduce the exponent, offset by 4 to avoid remainders of 0 ... WebFor instance, 24 + 123 has the last digit 7 as does 1231234 + 3, even though the two sums have completely di erent numbers; their last digits are the same, so the sum should have the same last ... In order to a get a \higher" power of 7, we can multiply a smaller one by 7. Since we only care about the nal digit, we can take the smaller one’s ...
WebOct 18, 2016 · Therefore you need to use BigInteger or write your own exponentiation function. The latter is the more desirable since the way more efficient way to compute the last digit is to reduce a modulo 10, b modulo 4, then take the power and then reduce modulo 10 again. This should even work within the range were floating-point arithmetic is … WebMay 12, 2024 · answered Find the last digit of 3278^123 Advertisement kartikharti1856 is waiting for your help. Add your answer and earn points. Answer No one rated this …
WebFeb 19, 2024 · Kudos. sthahvi wrote: Jai1903 wrote: ( ( 36472) 123!) ∗ ( ( 34767) 76!) Since we have to find last digit, we will find remainder when divided by 10. For ( ( 34767) 76!): 34767 fetches 7. Since we have 76! in power thus 7 2 gives 49 which gives -1 as remainder. Since 76! is multiple of 4 we get 1 as remainder.
WebJul 20, 2016 · 1. 3 100 = 9 50 = ( 1 − 10) 50 = 1 − 50 ⋅ 10 + ( 50 2) 10 2 − ⋯ = 1 + 10 ⋅ integer. so the last digit is 1. In fact it's easy to see from this that the last two digits are 01, and not too hard to see that the last three digits are 001 (because the first three terms of the expansion are 1 − 500 + 62500 = 62001 ). Share. the the music groupWebMay 21, 2024 · To find : The unit digit of the expression? Solution : First we determine the cyclicity of number 9. The cyclicity of 9 is 2. Now with the cyclicity number i.e. with 2 divide the given power . i.e. 85 ÷ 2 . The remainder will be 1. The required answer is 9 raised to the power 1 is 9. Therefore, The unit digit of is 9. the themseWebOct 4, 2024 · HOW TO FIND LAST TWO DIGITS of ANY POWER NUMBER SYSTEM FOR CAT SSC set a grammar and punctuation 1WebThe last digit repeats in a pattern that is 4 digits long: 7,9,3,1 7,9,3,1. Note that 358 358 divided by 4 4 is 89 89 with a remainder of 2, 2, so the pattern will repeat 89 89 times, … setag plymouthWebDec 3, 2024 · The units digit of any power of 5 remains 5 so the last digit of 15^15 will be 5. This implies that last digit of 12^12+13^13 will be 9 and that of 14^14×15^15 will be 0. Since 14^14×15^15 is definitely much greater than (12^12+13^13), (12^12+13^13)– (14^14×15^15) will be a negative number with a units digit of 1. set a good example to or forWebfind the unit digit of 3278^1237 - YouTube #RevoClasses #ShortTrickMaths #Aptitudefind the unit digit of 3278^1237Join the Telegram Channel by clicking the link... the the music bandWebJul 28, 2024 · Find last digit of a number with power First identify the pattern last digit (unit place) for power of numbers “N” From the above table we can observe as follow The last digit of power of 1, 5 & 6 is … the thenar eminence