A number when divided by 256 leaves a remainder of 141. Find the remainder when the same number is divided by 16.a)7b)11c)13d)17Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Let the quotient and the dividend be ‘q’ and ‘x’ respectively
⇒ x = 256q + 141
⇒ x = (16 × 16)q + (16 × 8) + 13
⇒ x = 16(16q + 8) + 13
∴ When the number is divided by 16, the remainder is 13

Answer

Let the quotient and the dividend be ‘q’ and ‘x’ respectively
⇒ x = 256q + 141
⇒ x = (16 × 16)q + (16 × 8) + 13
⇒ x = 16(16q + 8) + 13
∴ When the number is divided by 16, the remainder is 13

Answer

To find the remainder when a number is divided by 16, we need to understand the relationship between the remainders when the same number is divided by 256 and 16.

Let's assume the number we are considering is 'x'.

Given that when x is divided by 256, the remainder is 141, we can express this as:
x ≡ 141 (mod 256)

To find the remainder when x is divided by 16, we need to find a congruence relation involving x and 16.

We know that 256 is divisible by 16, so we can express 256 as a multiple of 16:
256 = 16 * 16

Now, let's substitute 256 in the congruence relation:
x ≡ 141 (mod (16 * 16))

Simplifying further:
x ≡ 141 (mod 16)

From this congruence relation, we can conclude that the remainder when x is divided by 16 is 141.

Therefore, the correct answer is option C, 141.

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