A number, when divided by 783, gives a remainder 48. What remainder would be…

Step-by-Step Solution

To find the remainder when a number is divided by a smaller divisor, we can use the property of remainders based on factors of the original divisor.

1. Express the number in terms of the first divisor:

   • Let the number be N. When N is divided by 783, it gives a remainder of 48.

   • This can be written as: N = 783 * k + 48, where k is the quotient.

2. Check the relationship between the divisors:

   • We need to find the remainder when N is divided by 29.

   • Notice that 783 is a multiple of 29: 783 / 29 = 27.

   • Therefore, N = (29 * 27 * k) + 48.

3. Simplify the expression:

   • We can further break down 48 into a multiple of 29 and a remainder:

   • 48 = (29 * 1) + 19.

   • Substituting this back into the expression for N:

   • N = (29 * 27 * k) + (29 * 1) + 19

   • N = 29 * (27k + 1) + 19.

4. Determine the remainder:

   • The equation shows that when N is divided by 29, the remainder is 19.