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What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 05:10
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What is the remainder obtained when \(63^{26}\) is divided by 16? A. 2 B. 1 C. 1 D. 8 E. 10
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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 06:35
rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 Hi.... 63 divided by 16 will leave a remainder of 1 as 64 is divisible by 16.. So 63*63*63....26times will leave a remainder of (1)*(1)*.....26times = \((1)^{26}=((1)^2)^{13}=1^{13}=1\) C
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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 06:42
chetan2u wrote: rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 Hi.... 63 divided by 16 will leave a remainder of 1 as 64 is divisible by 16.. So 63*63*63....26times will leave a remainder of (1)*(1)*.....26times = \((1)^{26}=((1)^2)^{13}=1^{13}=1\) C Hi Chetan sir, What's the concept of negative remainder?Why don't we assume remainder as 15 and then (63/16)*(63^25) Bold leaves a remainder of 15 and then no reminader. I have a concept gap here.Please help.



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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 06:59
(63^26) /16=(16*41)^26/16=(1)^26=1
So choice C



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What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 07:04
prabsahi wrote: chetan2u wrote: rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 Hi.... 63 divided by 16 will leave a remainder of 1 as 64 is divisible by 16.. So 63*63*63....26times will leave a remainder of (1)*(1)*.....26times = \((1)^{26}=((1)^2)^{13}=1^{13}=1\) C Hi Chetan sir, What's the concept of negative remainder?Why don't we assume remainder as 15 and then (63/16)*(63^25) Bold leaves a remainder of 15 and then no reminader. I have a concept gap here.Please help. Dear prabsahi\(\frac{63}{16} = 15\) And, \(\frac{63^{26}}{16} = \frac{63}{16}*\frac{63}{16}*\frac{63}{16}*\frac{63}{16}*\frac{63}{16}*\)..........26 Times... We know that \(\frac{63}{16} = 15\) So, \(\frac{63}{16}*\frac{63}{16} = \frac{225}{16}\) = Remainder \(1\) We may save \(\frac{63}{16}*\frac{63}{16}\) will always yeild 1 as remainder and we have 13 such sets of \(\frac{63}{16}*\frac{63}{16}\), thus, the result will be 1 , Answer must be (C) 1Hope this helps.
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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 07:19
prabsahi wrote: chetan2u wrote: rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 Hi.... 63 divided by 16 will leave a remainder of 1 as 64 is divisible by 16.. So 63*63*63....26times will leave a remainder of (1)*(1)*.....26times = \((1)^{26}=((1)^2)^{13}=1^{13}=1\) C Hi Chetan sir, What's the concept of negative remainder?Why don't we assume remainder as 15 and then (63/16)*(63^25) Bold leaves a remainder of 15 and then no reminader. I have a concept gap here.Please help. Reason, is that you have to get into big calculations then ... say with 1 as remainder we had ODD power 25 then the remainder would be 1, and remainder cannot be negative hence 161=15 We are taking negative remainder in initial calculations just to ease our calculations. Otherwise finally it has to be converted into positive remainder.
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What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 07:31
We can treat it this way
(641)^26
64^26 and some lengthy calculations in the end we have 1^26. everything in between 64^26 and 1^26 will be divisible by 16
Everything in this equation is divisible by 16 except for 1 so the remainder is 1
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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 07:51
rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 For the concept behind solving such questions, check: https://www.veritasprep.com/blog/2011/0 ... ekinyou/Also for negative remainders, see: https://www.veritasprep.com/blog/2014/0 ... thegmat/
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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 08:44



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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 09:17
chetan2u wrote: rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 Hi.... 63 divided by 16 will leave a remainder of 1 as 64 is divisible by 16.. So 63*63*63....26times will leave a remainder of (1)*(1)*.....26times = \((1)^{26}=((1)^2)^{13}=1^{13}=1\) C I am not able to understand another point.. I dont see 16 repeated in the denominator.Its occuring only once. say.. (63/16)*63^25 so first term can give say 1 as remainder later on its just 63^25 times..



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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 09:19
VeritasKarishma wrote: rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 For the concept behind solving such questions, check: https://www.veritasprep.com/blog/2011/0 ... ekinyou/Also for negative remainders, see: https://www.veritasprep.com/blog/2014/0 ... thegmat/ Many many many Thanks



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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 09:20
enochjason wrote: (63^26) /16=(16*41)^26/16=(1)^26=1
So choice C Also, another approach: A mod B ( the remainder of A divided by B) 63^25 mod 16 =(16*3+15)^25 mod 16 =15^25 mod 16 =15^(2*12+1) mod 16 =(225^12) * 15 mod 16 =[(16*14+1)^12] *15 mod 16 =(1^12) *15 mod 16 =1*15 mod 16 =15



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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 09:23
prabsahi wrote: chetan2u wrote: rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 Hi.... 63 divided by 16 will leave a remainder of 1 as 64 is divisible by 16.. So 63*63*63....26times will leave a remainder of (1)*(1)*.....26times = \((1)^{26}=((1)^2)^{13}=1^{13}=1\) C I am not able to understand another point.. I dont see 16 repeated in the denominator.Its occuring only once. say.. (63/16)*63^25 so first term can give say 1 as remainder later on its just 63^25 times.. You multiply the remainders ... Say a number is 3*5 so when divided by 3 remainders will become 0*2=0 But if number is 4*5.. remainder will become 1*2=2 check 4*5=20and 20 divided by 3 gives a remainder of 2 So you have to divide each term in numerator by the same denominator ...
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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 09:28
What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10[/quote]
Hi.... 63 divided by 16 will leave a remainder of 1 as 64 is divisible by 16.. So 63*63*63....26times will leave a remainder of (1)*(1)*.....26times = \((1)^{26}=((1)^2)^{13}=1^{13}=1\)
C[/quote]
I am not able to understand another point..
I dont see 16 repeated in the denominator.Its occuring only once. say.. (63/16)*63^25
so first term can give say 1 as remainder later on its just 63^25 times..[/quote]
You multiply the remainders ... Say a number is 3*5 so when divided by 3 remainders will become 0*2=0 But if number is 4*5.. remainder will become 1*2=2 check 4*5=20and 20 divided by 3 gives a remainder of 2
So you have to divide each term in numerator by the same denominator ...[/quote]
Perfect..This was really very helpful.
Many many many Thanks !!



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Re: What is the remainder obtained when 63^26 is divided by 16?
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29 Oct 2018, 16:54
rencsee wrote: What is the remainder obtained when \(63^{26}\) is divided by 16?
A. 2 B. 1 C. 1 D. 8 E. 10 This can be written as 1^26 because 63 leaves 15 or 1 remainder with 16. 1^even is 1. Answer is 1. C.




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