What is the greatest possible positive integer n if 16^n divides (44)^44 without leaving a remainder.
a. 1?
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Answer:
22
Step-by-step explanation:
What is the greatest possible positive integer n if 16^n divides (44)^44 without leaving a remainder.
16ⁿ Divides 44⁴⁴
44⁴⁴ = (4 * 11)⁴⁴
11 is a prime number
= 4⁴⁴ * 11⁴⁴
= 4²ˣ²² * 11⁴⁴
= 16²² * 11⁴⁴
Maximum value of n = 22
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