A number when divided by 258 gives a remainder equal to 87. Find the remainder when the same number is divided by 43.

Step 1: Understand the problem The problem is asking for the remainder when a certain number is divided by 43. We know that this number, when divided by 258, gives a remainder of 87.

Step 2: Use the property of remainders The property of remainders states that if a number gives a remainder r when divided by a divisor d, then it will give the same remainder when divided by any factor of d.

Step 3: Check if 43 is a factor of 258 43 is not a factor of 258. However, 43 is a factor of 258 - 87 = 171. This means that the remainder when the number is divided by 258 is the same as the remainder when the number is divided by 171.

Step 4: Check if 43 is a factor of 171 43 is a factor of 171 (171 = 43 * 4).

Step 5: Use the property of remainders Since 43 is a factor of 171, the remainder when the number is divided by 43 is the same as the remainder when the number is divided by 171, which is 87.

So, the remainder when the same number is divided by 43 is 87.