Question

Find the highest power of 5 which can divide 22! + 17000!
a) 2
b) 4
c) 85
d) 250

Answer 1

The highest power of 5 which can divide 22!+17000=4

Step-by-step explanation:

$22!+17000$

Formula:$n!=n(n-1)(n-2)...2\cdot 1$

$22\cdot 21\cdot 20..\cdot 15\cdot 14..\cdot 10\cdot..5\cdot 4\cdot 3\cdot 2\cdot 1$

Multiple of 5 in 22! are

20,15,10,5

Power of 5 which divided 22!=$5\times 5\times 5\times 5=5^4$

$17000=17\times 2^3\times 5^3$

Power of 5 which divide 17000=3

Lcm$(5^4,5^3)=5^4$

Therefore, the highest power of 5 which can divide 22!+17000=4

#Learns more:

https://brainly.in/question/14345211:answered by Siddharta

Answer 2

Option (b) 4.

Highest power of 5 which divides 22! + 17000! is 4.    

Given

To find the hightest power of 5 which can divide 22! + 17000!

5 multiples in 22! is

20,15,10,5 -----> 5×5×5×5 = $5^4$

5 multiples in 17000!

17000! -----> 17×2³×5³

Taking LCM for power of 5, multiples of 5 in 22! and 17000! is

LCM ( $5^4$ , $5^3$ ) = $5^4$.

Therefore, highest power of 5 which divides 22! + 17000! is 4.

To learn more...

brainly.in/question/14345211