The exponent can only be found in the context of a base. But there is no base specified and so there can be no clear answer.
On possible answer is that 262144 = 512^2 so, with the base 512, the exponent is 2.
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The answer is 262144.
You cannot know that. It could be base 10.
262,144 = 2.62144 x 10^5262144 is standard notation for 86 (exponential notation), where 8 is the base and 6 is the exponent.
Numbers which are divisible by 262144 are the multiples of 262144. e.g. 262144, 524288, 786432 etc.
262144 = 2.62144 * 105