The number of zeros at the end of the product will be:

12 x 18 x 15 x 40 x 25 x 16 x 55 x 105

Given:

Product = 12 × 18 × 15 × 40 × 25 × 16 × 55 × 105

Formula used:

The number of zeros at the end of a product is determined by the number of pairs of 2s and 5s in its prime factorization.

Calculations:

Prime factorization of each number:

12 = 2 × 2 × 3 = 2² × 3

18 = 2 × 3 × 3 = 2 × 3²

15 = 3 × 5

40 = 2 × 2 × 2 × 5 = 2³ × 5

25 = 5 × 5 = 5²

16 = 2 × 2 × 2 × 2 = 2⁴

55 = 5 × 11

105 = 3 × 5 × 7

Combine all prime factors:

Total powers of 2 = 2 + 1 + 3 + 4 = 10 (from 2², 2¹, 2³, 2⁴)

Total powers of 5 = 1 + 1 + 2 + 1 + 1 = 6 (from 5¹, 5¹, 5², 5¹, 5¹)

The number of zeros is limited by the factor that appears fewer times. In this case, it's the number of 5s.

⇒ Number of zeros = 6

∴ The number of zeros at the end of the product will be 6.