Compute the missing divisor: 62976 divided by N equals 123 (that is, 62976 ÷ N = 123). What is the value of N?

Introduction / Context:
This is a direct division problem presented as a missing factor question. Solving requires rearranging to N = 62976 / 123 and computing the quotient accurately. Recognizing powers of two may speed up checking the candidate options.

Given Data / Assumptions:

• 62976 ÷ N = 123.
• N is a positive integer.
• We must find N.

Concept / Approach:
Rearrange the relation to isolate N. Then compute the division or check by multiplication with candidate options. Since 512 is a familiar power of two (2^9), quickly testing 123 * 512 is efficient.

Step-by-Step Solution:

Verification / Alternative check:
Perform long division 62976 ÷ 123 to confirm the quotient 512 with no remainder. This validates the selection.

Why Other Options Are Wrong:
412, 502, and 522 do not produce 62976 when multiplied by 123. 123 would imply 123 * 123 = 15129, which is far too small.

Common Pitfalls:
Arithmetic slips in multiplication or assuming that the divisor must be near 123. Using estimation helps but should be confirmed by exact multiplication.

Final Answer:
512