Find a common factor of (4^743 + 4^343) and (4^747 + 4^347).

Given data

• S1 = 4^743 + 4^343
• S2 = 4^747 + 4^347

Concept / Approach

• Factor out common powers of 4 and compare.

Step-by-step factorization

S1 = 4^343(4^400 + 1)S2 = 4^347(4^400 + 1) = 4^343 · 4^4 · (4^400 + 1)Thus, 4^343(4^400 + 1) divides both S1 and S2.

Why alternatives fail

• 4^343(4^400 − 1): the (4^400 − 1) factor is not present in either expression.
• 4^344(4^400 + 1): divides S2 but not S1 (S1 has only 4^343).
• 4^400 − 1: unrelated to the given sums.

Final Answer

Common factor = 4^343(4^400 + 1).