Question

A common factor of $(127^{97}+97^{97})$ and $(257^{166}-243^{166})$ is∶

• A. 14
• B. 15
• C. 20
• D. 25

Answer 1

Answer:

A. 14

As we know,

(a³ + b³) = (a + b) (a² + b² – ab)

(127⁹⁷ + 97⁹⁷) is divisible by (127 + 97 = 224)

As we know,

(a² – b²) = (a – b) (a + b)

(257¹⁶⁶ – 243¹⁶⁶) is divisible by (257 – 243 = 14)

⇒ 224 = $2\times{2}\times{2}\times{2}\times{2}\times{7}$

⇒ 14 = $2\times{7}$

Common factor = 2 $\times$ 7 = 14