Question

If n! =840*4320,then find the value of n.

Answer 1

n! =840× 4320
First of all just factorise it to low integers especially to prime numbers.
=(7×3×2×2×2×5)×(2×3×3×3×2×4×2×5)
Then arrange numbers in the order 1,2,3,4,......
here i will show

To get 6 ,you can adjust a 3 and 2 if available. For 8 ,choose 4 and 2 or 2 ×2×2...
Like wise ..
here

=2×3×(2×2)×5×(2×3)×7×(4×2)×(3×3)×(5×2)
=2×3×4×5×6×7×8×9×10

so for a adjustment, we can add 1 also bcz no change in answer.

=1×2×3×4×5×6×7×8×9×10
=10!

so n!=10!

so n=10.

Like if satisfied