Question

what is the highest power of 21 in 342!​

Answer 1

Answer:

There is only one power of [math]7[/math] (or any other number, for that matter) in the prime factorization (or any huge number).

Step-by-step explanation:

hope it will help you....

Answer 2

Answer: Highest power of 21 in 342!=55

Step-by-step explanation:

• if p is a prime number, then the highest power of p in n!

          =(n/p)+(n/p²)+(n/p³)+...............

• Prime factors of 21 are 7 and 3.
• So highest power of 21 =max(power of 3 in 342!, power of 7 in 342!)

• Power of 3 in 342!=(342/3)+(342/9)+(342/27)+(342/81)+(342/243)

                                      =114+38+12+4+1=169

• Power of 7 in 342!=(342/7)+(342/49)+(342/342)

                                      =48+6+1=55

• Highest power of21 in 342!=max(169,55)=55