Question

$$Find the number of zeros at the right end of

$12^5\times25^2\times8^3\times35^2\times14^3$

• A. 5
• B. 7
• C. 6
• D. 8

Answer 1

Answer:

C. 6

To find the zeros at the right end we have to prime factorize each term

$12^5\times25^2\times8^3\times35^2\times14^3$

$=(2^2\times3)^5\times(5^2)^2\times(2^3)^3\times(5\times7)^2\times(2\times7)^3$

$=2^{10}\times3^5\times5^4\times2^9\times7^2\times5^2\times7^3\times2^3$

$=2^{22}\times3^5\times5^6\times7^5$

the number of zeros at the right end = powers of 5 = 6

$$Since 0 is obtained when 5 is multiplied by 2