Question

The number, among the following, that divides 7¹² - 2²⁴ is
1. 32
2. 33
3. 34
4. 35
5.

Answer 1

Correct Answer - Option 2 : 33

Given:

712 - 2²⁴

Concept used:

a³ - b³ = (a - b) (a² + ab + b²)

(a -b) divides the (a³ - b³).

Calculation:

⇒ 712 - 2²⁴

⇒ (7⁴)³ - (2⁸)³

From above equation, the factors are

⇒ (7⁴) - (2⁸)

⇒ 2401 - 256

⇒ 2145

By checking the option the number 2145 is divisible by option (2)

⇒ 2145/33

⇒ 65

∴ The number that divides 712 - 224 is 33.