Problem:
How many zeros are at the end of the product
25×25×25×25×25×25×25×8×8×8?
Answer Choices:
A. 3
B. 6
C. 9
D. 10
E. 12
Solution:
Since 2×5=10, each zero at the end of the product comes from a product of 2 and 5 in the prime factorization of the number. Since 25=5×5 and 8=2×2×2, it follows that there are fourteen factors of 5 and 9 factors of 2. This yields 9 pairs of 2×5 and results in 9 zeros at the end of the product.
OR
Multiplying the given numbers using a calculator gives an answer equivalent to 3.125×1012 which equals 3,125,000,000,000. This results in 9 zeros at the end of the product.