On dividing 15^209 by 7, remainder will be

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13 Mar 2012 remainder On dividing 15^209 by 7, remainder will be: OPtion
1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 0
8) not possible to find; Correct Option: 1 Best Solution (17)

J.P.Raja Suresh 12 years AGO

=> no need to consider the power
=> whenever we use mod as 7
=> no jus leave out 209
=> 15 mod 7
=> 15 mod 7 =1
=> Ans : 1 (Options : 1)

Like? Yes (9) | No (1)

Vignesh 12 years AGO

Dividing any power of 15 by 7, we get remainder 1 only.

Because 15/7 we get REMAINDER 1 only.

Like? Yes (3) | No

prem kumar.s 12 years AGO

15^1/7 remainder=1
15^2/7 remainder=1
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.
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so 15^209 remainder=1

Like? Yes (3) | No

Mageshkumar 12 years AGO

15^1 by 7, remainder=1
15^2 by 7, remainder=1
15^3 by 7, remainder=1.
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.
.
.
so 15^209 by 7, remainder=1

Like? Yes (2) | No

Ashish Pandey 12 years AGO

15/7remainder=1
(15^2)/7 remainder=1
(15^3)/7 remainder=1
in the same way.
(15^209)/7 remainder=1

Like? Yes (1) | No

Balakrishnan M 12 years AGO

On dividing 15^(any number) by 7 The remainder will be 1.

Like? Yes (1) | No

arunraj 12 years AGO

(15)^1 mod 7=1
(15)^2 mod 7=1
(15)^n mod 7=1
=> m^n mod x== m mod x
so 15 mod 7=1

Like? Yes (1) | No

nithya 12 years AGO

when divide a powers of 15 by 7 remainder is 1

Like? Yes (1) | No

Tijo Jose 12 years AGO

By Fermat's Little Theorem, for a prime p,
a^(p-1) mod p = 1
So, 15^6 mod 7 = 1
Taking 35th power on both sides,
(15^6 mod 7)^35 = 1^35
15^210 mod 7 = 1
(15 mod 7) * (15^209 mod 7) = 1
1 * (15^209 mod 7) = 1
Or, (15^209 mod 7) = 1

Like? Yes (1) | No

B.Senthil Kumar 12 years AGO

15^1=15%7=1
15^3=3375%7=1
15^5=759375%7=1
so the answer is option 1

Like? Yes (1) | No

sugumar 12 years AGO

15^1=15/7=1
15^2=225/7=1
15^3=3375/7=1
so divide by 7 the remainder is 1

Like? Yes (1) | No

Harshit Dwivedi 12 years AGO

the remainder of any no. and the same no. with power are equal.
so, remainder of (15^209)/7 is equal to 15/7
i.e. 1

Like? Yes (1) | No

Rakesh Kumar Kohli 12 years AGO

When 15 is divided 7 then Quotient is 2 and reminder is 1 ( as 15 = 2*7 + 1). When we will multiply by 15, it means quotient portion is multiplied by 15 which will be divisible by 7 and reminder 1 when multiplied by 15 gives 15 which on division by 7 will again give reminder 1. If we carry on this process any number of times we will always get reminder as 1.
Hence Ans. 1) 1

Like? Yes (1) | No

J.P.Anitha 12 years AGO