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Question

Question: It is a suprising fact that 1x2x3x4x5x6=8x9x10. It is even more suprising that 8x9x10x11x12x13x14 is equal to another such product of consecutive whole numbers. What is the smallest number in this product.

Answer: 63

Pls let me know if you have any formula to quickly arrive at the answer

Thanks!

Answer 1

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Answer 2

Divide the numbers into their prime numbers, and then re-organize and multiply them until you get another such consecutive list.

Like in your second example:

8x9x10x11x12x13x14

=> (2x2x2)x(3x3)x(5x2)x11x(3x2x2)x13x(2x7)

=> (7x3x3)x(2x2x2x2x2x2)x(5x13)x(11x3x2)

=> 63x64x65x66

You could, of course, program your graphing calculator or computer to computer such numbers in a much shorter time.