Factorials

Question 1

1!

Answer 1

1

Question 2

0!

Answer 2

1

Question 3

Factorials

Answer 3

Just a set of consecutive integers

Question 4

Remember, set of consecutive integers

Answer 4

divsible by any of its integers or any product of a combination of its integers
To do this, you will need to prime factorize the integers of factorial and place over the prime factorization of no you are dividing by
OR - shortcut: assume n!/3^y………..so 21!/3^y……
21/3^1 = Quotient is 7
21/3^2 = Quotient is 2 (ignore remainder)
21/3^3 = Quotient is 0 - STOP
add 7 + 2 = 9 so 9 ‘3’s’ in 21!
answer is 3^9; y=9
If divisor is not a prime number, prime factorize it into prime numbers, and use largest prime factor to determine quantity (because you want pairs, which are necessarily limited by larger prime factor)
and if divisor (with or without Prime factorization) has a power greater than one (eg x^nw), then pretend has no power (use just base) for the division, then once you have quotients and hvae added them up, use inequality: result of adding wn <= Qs; n <= blahblah

Question 5

the product of any set of n positive consecutive integers

Answer 5

is always divisible by n!