Question

Number of zero's in the product of
$5\times 10\times 25\times 40\times 50\times 55\times 65\times 125\times 80$

• A. $8$
• B. $9$
• C. $12$
• D. $13$

Answer 1

The correct option is B $9$

$5\times 10\times 25\times 40\times 50\times 55\times 65\times 125\times 80$
$=5\times 2\times 5\times 5^2\times 2^3\times 5\times 2\times 5^2\times 11\times 5\times 13\times 5\times 5^3\times 2^4\times 5$
$=2^9\times 5^{13}\times 11\times 13=(2\times 5{)}^9\times 5^4\times 11\times 13$

As we know that zeroes are formed by the product of a $2$ and a $5$ i.e. $2$ x $5$.

Therefore, number of zeroes depends on the number of pairs of $2$'s and $5$'s that can be formed in the given product.

Since $9$ pairs of $2$'s and $5$'s are formed in the given product, hence there will be $9$ zeroes in the given product.