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What is the remainder when (123451)6 is divided by 5?
- a)1
- b)0
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
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What is the remainder when (123451)6 is divided by 5?a)1b)0c)3d)4Corre...
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What is the remainder when (123451)6 is divided by 5?a)1b)0c)3d)4Corre...
To find the remainder when (123451)6 is divided by 5, we need to determine the value of (123451)6 modulo 5.
First, let's understand what (123451)6 means. The number (123451)6 is written in base 6, which means that each digit in the number is multiplied by a power of 6. The rightmost digit is multiplied by 6^0, the next digit is multiplied by 6^1, the next digit is multiplied by 6^2, and so on. So, (123451)6 can be expanded as follows:
(123451)6 = 1 * 6^5 + 2 * 6^4 + 3 * 6^3 + 4 * 6^2 + 5 * 6^1 + 1 * 6^0
Now, we can simplify this expression by evaluating the powers of 6:
(123451)6 = 1 * 6^5 + 2 * 6^4 + 3 * 6^3 + 4 * 6^2 + 5 * 6^1 + 1 * 6^0
= 1 * 7776 + 2 * 1296 + 3 * 216 + 4 * 36 + 5 * 6 + 1 * 1
= 7776 + 2592 + 648 + 144 + 30 + 1
= 11291
Now, to find the remainder when 11291 is divided by 5, we divide 11291 by 5 and find the remainder:
11291 ÷ 5 = 2258 remainder 1
Therefore, the remainder when (123451)6 is divided by 5 is 1.
First, let's understand what (123451)6 means. The number (123451)6 is written in base 6, which means that each digit in the number is multiplied by a power of 6. The rightmost digit is multiplied by 6^0, the next digit is multiplied by 6^1, the next digit is multiplied by 6^2, and so on. So, (123451)6 can be expanded as follows:
(123451)6 = 1 * 6^5 + 2 * 6^4 + 3 * 6^3 + 4 * 6^2 + 5 * 6^1 + 1 * 6^0
Now, we can simplify this expression by evaluating the powers of 6:
(123451)6 = 1 * 6^5 + 2 * 6^4 + 3 * 6^3 + 4 * 6^2 + 5 * 6^1 + 1 * 6^0
= 1 * 7776 + 2 * 1296 + 3 * 216 + 4 * 36 + 5 * 6 + 1 * 1
= 7776 + 2592 + 648 + 144 + 30 + 1
= 11291
Now, to find the remainder when 11291 is divided by 5, we divide 11291 by 5 and find the remainder:
11291 ÷ 5 = 2258 remainder 1
Therefore, the remainder when (123451)6 is divided by 5 is 1.
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What is the remainder when (123451)6 is divided by 5?a)1b)0c)3d)4Correct answer is option 'A'. Can you explain this answer?
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