The remainder when 2^340 is divided by 341 is: Option 1: 0 Option 2: 1 Option 3: -1 Option 4: 2

Answer: 1. Solution: We need to find the remainder when 2^340 is divided by 341. Now, 2^340 = (2^10)^34 = 1024^34 Also, 1024 = 341 x 3 + 1 So, 1024^34 = (341 x 3 + 1)^34 Hence, (341 x 3 + 1)^34 1^34 ±od341 2^340 1 ±od341 Therefore, the remainder is 1.

Arithmetic

Numericals

Medium

applied

The remainder when $2^{340}$ is divided by 341 is:

-1

✅ Correct Option: 2

We need to find the remainder when $2^{340}$ is divided by $341$ .

Now,

$2^{340} = (2^{10})^{34} = 1024^{34}$

Also,

$1024 = 341 \times 3 + 1$

So,

$1024^{34} = (341 \times 3 + 1)^{34}$

Hence,

$(341 \times 3 + 1)^{34} \equiv 1^{34} \pmod{341}$

$\Rightarrow 2^{340} \equiv 1 \pmod{341}$

Therefore, the remainder is $\boxed{1}$ .

2025: 29 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Unit's digit of $2^{11}$	(I) 2
(B) Unit's digits of $11^{132}$	(II) 1
(C) Remainder when $71 \times 73 \times 75$ is divided by 23	(III) 4
(D) Remainder when $7^{30}$ is divided by 5	(IV) 8

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Solution

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The remainder when $2^{340}$ is divided by 341 is: