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47−44^7-447−4​ is NOT a multiple of:
Question

4744^7-4​ is NOT a multiple of:

A.

4

B.

8

C.

7

D.

2

Correct option is B

Given:
Expression: 4⁷ - 4
Solution:
4⁷ - 4 can be written as 4⁷ - 4¹ = 4(4⁶ - 1)
4⁶ - 1 = (4³ + 1)(4³ - 1)
So, 4(4⁶ - 1) = 4(4³ + 1)(4³ - 1)
Factorize 4³ - 1 = (4 - 1)(4² + 4 + 1) = 3 ×\times​ 21
​And 4³ + 1 = (4 + 1)(4² - 4 + 1) = 5 ×\times13
So, 4(4⁶ - 1) = 4 ×\times 3 ×\times 5 ×\times13 ×\times 21
From the above factors, we can see that 4⁷ - 4 is a multiple of 4, 3, 5, 13 and 21.
So, 4⁷ - 4 is NOT a multiple of 8. So the correct answer is B.

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