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Find the remainder when 4^96 is divided by 6.
a)0
b)2
c)3
d)4
Correct answer is option 'D'. Can you explain this answer?
a)0
b)2
c)3
d)4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the remainder when 4^96 is divided by 6.a)0b)2c)3d)4Correct answe...
496/6, We can write it in this form
(6 - 2)96/6
Now, Remainder will depend only the powers of -2. So,
(-2)96/6, It is same as
([-2]4)24/6, it is same as
(16)24/6
Now,
(16 * 16 * 16 * 16..... 24 times)/6
On dividing individually 16 we always get a remainder 4.
So,
(4 * 4 * 4 * 4............ 24 times)/6.
Hence, Required Remainder = 4.
NOTE: When 4 has even number of powers, it will always give remainder 4 on dividing by 6.
(6 - 2)96/6
Now, Remainder will depend only the powers of -2. So,
(-2)96/6, It is same as
([-2]4)24/6, it is same as
(16)24/6
Now,
(16 * 16 * 16 * 16..... 24 times)/6
On dividing individually 16 we always get a remainder 4.
So,
(4 * 4 * 4 * 4............ 24 times)/6.
Hence, Required Remainder = 4.
NOTE: When 4 has even number of powers, it will always give remainder 4 on dividing by 6.
Most Upvoted Answer
Find the remainder when 4^96 is divided by 6.a)0b)2c)3d)4Correct answe...
Finding the Remainder of 496 When Divided by 6
To find the remainder when 496 is divided by 6, we need to follow the following steps:
Step 1: Divide 496 by 6 using long division or a calculator.
496 ÷ 6 = 82 with a remainder of 4
Step 2: The remainder obtained in step 1 is the answer.
Therefore, the remainder when 496 is divided by 6 is 4.
Conclusion
Option D, which is 4, is the correct answer.
To find the remainder when 496 is divided by 6, we need to follow the following steps:
Step 1: Divide 496 by 6 using long division or a calculator.
496 ÷ 6 = 82 with a remainder of 4
Step 2: The remainder obtained in step 1 is the answer.
Therefore, the remainder when 496 is divided by 6 is 4.
Conclusion
Option D, which is 4, is the correct answer.
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Community Answer
Find the remainder when 4^96 is divided by 6.a)0b)2c)3d)4Correct answe...
Let N= 4^96, this question can be changed to 2*(4^95) is being divided by 3 ( cancelling the common factor 2) . Now remainder when 2*(3+1)^95 is divided by 3 is 2.
So we can write,
2*(4^95 ) = 3k +2
=> 4*(4^95) = 6k+4 ( multiply both sides by 2)
so remainder is 4.
So we can write,
2*(4^95 ) = 3k +2
=> 4*(4^95) = 6k+4 ( multiply both sides by 2)
so remainder is 4.
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Find the remainder when 4^96 is divided by 6.a)0b)2c)3d)4Correct answer is option 'D'. Can you explain this answer?
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