What is the exponent of the greatest power of 40 that will divide into 80! with no remainder ?

19

Step-by-step explanation: For each power of 40, you need 3 prime factors of 2 and 1 prime factor of 5.

In 80, the number of factors of 5 is 16+3 = 19.

In 80, the number of factors of 2 is 40+20+10+5+2+1 = 78.

The number of prime factors of 2 in 80! is more than 3 times the number of prime factors of 5; that means the number of prime factors of 5 is what limits the power of 40 that divided into 80! gives a whole number answer. So