Wt's unit digit of 2^3^4^5....
I am getting 6 as answer but d ans is 2..can u help?
Q2. Hey can u please tell me how would u fing the unit digit of something like 5689^2456 ? (i.e 5689 2456
find d Number of zeroes at the end of 124*126*128*...*1002..plz help Thanks & Regards Chandan Kumar
Humraj
Hi!
Number of zeroes at the end of 124x126x128................x1002 is 110.
if my ans is right, plz reply.
and i cant understand ur second pro.
what is 2^3^4^5........
i don't kno d ans....so plz tell ur approach how did u find it?
for the 2nd q
what's the unit digit of 2^3^4^5
124x126x128............................x1002
= (2440)(62x63x64...........................x501)
= (2440)(501! / 61!)
The highest power of 5 of 501! and 61! are 124 and 14 respectively.
The highest power of 5 of (501! /61!) is 110.
Wt's unit digit of 2^3^4^5....??
ANS:
Since cylicity of '2' is 4 i.e(2,4,8,6)..so ve divide the power by 4, we get
3^4^5/4 = (-1)^4^5/4 = 1/4 =Rem 1..i.e 1st digit in cyclicity n that is 2 ..hence ans is 2.
:-)
what is this cyclicity rule?
can u pls explain in breif
can u pls explain in breif pls
CYCLICITY CONCEPT:
I'll try n explain it wid some examples...
Let us consider -2
Unit digit of 2 =2 Unit digit of 25 = 2
Unit digit of 22 = 4 Unit digit of 26 = 4
Unit digit of 22 = 8 Unit digit of 27= 8
Unit digit of 24 = 6 Unit digit of 28 = 6
So as u can see above the unit digit repeats itself after every 4TH power of "2". Hence its cylicity is 4.
Let us consider -3
Unit digit of 3 = 3 Unit digit of 35 = 3
Unit digit of 32 = 9 Unit digit of 36 = 9
Unit digit of 32 = 7 Unit digit of 37= 7
Unit digit of 34 = 1 Unit digit of 38 = 1
So as u kan see above the unit digit repeats itself after every 4TH power of "3". Hence its cylicity is also 4.
Similarly u kan find the cyclicity of other digits as well..n u'll get
Cyclicity of 5 =1
Cyclicity of 6 =1
Cyclicity of 7 =4
Cyclicity of 8 =4
Cyclicity of 9 =2
Merci beaucoup
Check out the following post to know how to solve many similar questions
http://www.cat4mba.com/node/4768
Thanx ya...
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find d Number of zeroes at the end of 124*126*128*...*1002..plz help
Thanks & Regards
Chandan Kumar
Humraj
Hi!
Number of zeroes at the end of 124x126x128................x1002 is 110.
if my ans is right, plz reply.
and i cant understand ur second pro.
what is 2^3^4^5........
i don't kno d ans....so plz tell ur approach how did u find it?
for the 2nd q
what's the unit digit of 2^3^4^5
Humraj
124x126x128............................x1002
= (2440)(62x63x64...........................x501)
= (2440)(501! / 61!)
The highest power of 5 of 501! and 61! are 124 and 14 respectively.
The highest power of 5 of (501! /61!) is 110.
Wt's unit digit of 2^3^4^5....??
ANS:
Since cylicity of '2' is 4 i.e(2,4,8,6)..so ve divide the power by 4, we get
3^4^5/4 = (-1)^4^5/4 = 1/4 =Rem 1..i.e 1st digit in cyclicity n that is 2 ..hence ans is 2.
:-)
what is this cyclicity rule?
can u pls explain in breif
what is this cyclicity rule?
can u pls explain in breif pls
CYCLICITY CONCEPT:
I'll try n explain it wid some examples...
Let us consider -2
Unit digit of 2 =2 Unit digit of 25 = 2
Unit digit of 22 = 4 Unit digit of 26 = 4
Unit digit of 22 = 8 Unit digit of 27= 8
Unit digit of 24 = 6 Unit digit of 28 = 6
So as u can see above the unit digit repeats itself after every 4TH power of "2". Hence its cylicity is 4.
Let us consider -3
Unit digit of 3 = 3 Unit digit of 35 = 3
Unit digit of 32 = 9 Unit digit of 36 = 9
Unit digit of 32 = 7 Unit digit of 37= 7
Unit digit of 34 = 1 Unit digit of 38 = 1
So as u kan see above the unit digit repeats itself after every 4TH power of "3". Hence its cylicity is also 4.
Similarly u kan find the cyclicity of other digits as well..n u'll get
Cyclicity of 5 =1
Cyclicity of 6 =1
Cyclicity of 7 =4
Cyclicity of 8 =4
Cyclicity of 9 =2
:-)
Merci beaucoup
Check out the following post to know how to solve many similar questions
http://www.cat4mba.com/node/4768
Thanx ya...
:-)
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