Good day, young scholars of this esteemed educational establishment. Today, I present to you a conundrum most intriguing, one that shall test the very limits of your mental faculties. In an age where the numerical calculator is but a dream, you are to rely solely upon your intellect and the power of reasoning.

Consider, if you will:

A. The grand product of all the whole numbers commencing from the humblest 1 and concluding with the noble 10. This, as you well know, is represented as 10 factorial.

B. The total number of seconds that elapse during the span of six weeks.

Without resorting to the barbaric act of complete multiplication, and with the utmost elegance, deduce: Which of these two numbers towers above the other in magnitude?

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