The product of all the prime numbers between 1 and 100 is equal to P. What is the remainder when P is divided by 16?
Skip the first prime 22 and look for the product modulo 88. The twenty-four odd primes <100<100 are
Modulo 88, these are
so their product is
(where we might profit from using x2≡1(mod8)x2≡1(mod8) for odd xx). Thus P≡6(mod16)P≡6(mod16).
Thus the Answer you are looking for