Question

When a number is divided by 893, the remainder is 193. What will be the remainder when it is divided by 47?

a)3
b)5
c)25
d)33

Answer 1

To find the remainder when a number is divided by 47, we can use the concept of modular arithmetic. The remainder when the number is divided by 47 will be the same as the remainder when 193 is divided by 47, which is 25.

Step-by-step explanation:

To find the remainder when a number is divided by 47, we can use the concept of modular arithmetic. Since the remainder when the number is divided by 893 is 193, we can express the number as 893n + 193, where n is an integer. Now, let's divide this expression by 47:

(893n + 193) ÷ 47 = 19n + (193 ÷ 47)

This tells us that the remainder when the number is divided by 47 will be the same as the remainder when 193 is divided by 47. Evaluating this division, we find that the remainder is 25.

Therefore, the correct answer is c) 25.