How to find Number of Zeroes in an Expressions

How to find Number of Zeroes in an Expressions

Let a given expression is 13 × 15 × 22 × 125 × 44 × 35 × 11. You can see given expression is a products of numbers.
Now, we need to find number of zeroes in the product. Therefore we can rewrite the product as follows,
13 × 15 × 22 × 125 × 44 × 35 × 11 = {13 × 5 × 3 × 2 × 11 × 5 × 5 × 5 × 2 × 2 × 5 × 7 × 11}
13 × 15 × 22 × 125 × 44 × 35 × 11 = {2³ × 5⁵ × 13 × 3 × 11 × 7 × 11}

Zeroes are formed by the combination of (2 × 5). It means whenever we get a pair of 2 and 5, we always get a zero for the pair. Hence, the number of zeroes will depend on the number of pairs of 2’s and 5’s that can be formed. In above expression, there are three twos and five fives. Hence we shall able to form only three pairs of (2 × 5). Hence number of zeroes in the product will be 3.

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