How many zeros are at the end of 459 · 885? Explain how you can answer this question without actually computing the number. (Hint: 10 = 2 · 5.) When this number is written in ordinary decimal form, each 0 at its end comes from a factor of , or one factor of 2 and one factor of . Since there are factors of 2 and factors of 5, there are exactly factors of 10 in the number. This implies that the number ends with zeroes.

Step-by-step explanation:

If the multiplication of two numbers has the zero at the end, one of them will have a factor of 2 and the other number will have the factor of 5.

Example: Multiplication of 25 and 8.

                Factors of 25 = 5 × 5 [5 is a factor of 25]

                Factors of 8 = 2 × 2 × 2 [2 is a factor of 8]

Multiplication of 8 × 25 = 200 [Zero at the end]

Two numbers are 459 and 885.

Factors of 459 = 3 × 3 × 3 × 17

Factors of 885 = 3 × 5 × 59

[Since, 2 is not a factor in both the numbers multiplication of the numbers will not have 0 at the end]

459 × 885 = 406215

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