When a four digit number is divided by 65, it leaves a remainder of 29. If the same number is divided by 13, the remainder would be______a)0b)3c)5d)7Correct answer is option 'B'. Can you explain this answer?

Question

Answer

3

Answer

Modulo Arithmetic - Since 65 is multiple of 13, same remainder will come (29), just we need to further divide by 13..... So effectively 29 mod 13 = 3 will come.

Answer

According to question we need a 4 digit no and also on dividing it must give reminder 29
so 65×100=6500(a 4digit no.)
add 29 to it we get 6529
now divide 6529 with 13
get reminder

Answer

Assume digit is 1000
Y= Q*D+R so
Q=Y*D+R
here Y is dividend
Q is Quotient
D is divider
R is remainder
65*1000+29=65029
65029÷13 = Q=65002, R = 3

Answer

Corect answer is option. B

Answer

65*100=6500+29=6529
which gives remainder 29
6529/13
gives remainder 3

Answer

Because 65 is completely divisible by 13
And 29 divide by 13's remainder is 3

Answer

To find the remainder when a four-digit number is divided by 65, we need to understand the concept of remainders and how they are affected by division.

Let's assume the four-digit number is represented by ABCD, where A, B, C, and D are the thousands, hundreds, tens, and units digits respectively.

Remainder when divided by 65:
When we divide ABCD by 65, the remainder is given by the equation:

Remainder = (65 * Quotient) + Remainder

Here, Quotient represents the whole number obtained after division, and Remainder represents the remainder left after division.

Given that the remainder is 29, we can write the equation as:

29 = (65 * Quotient) + Remainder

Simplifying this equation, we have:

29 = 65 * Quotient + 29

Subtracting 29 from both sides, we get:

0 = 65 * Quotient

Since the remainder is 0 when divided by 65, we can conclude that the number ABCD is divisible by 65.

Remainder when divided by 13:
Now, let's consider the remainder when the same four-digit number is divided by 13.

To find the remainder, we can apply the same concept as before:

Remainder = (13 * Quotient) + Remainder

However, since we know that ABCD is divisible by 65 (as the remainder is 0), it will also be divisible by 13, as 65 is a multiple of 13.

This means that when ABCD is divided by 13, the remainder will also be 0.

Therefore, the correct answer is option 'A' (0) because when the four-digit number is divided by 13, the remainder will be 0.

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