4. Without calculating the product: 1.2.3.4.5.6.7.8.9.10.11$\cdot$12.13, find its last two digits.
Solution. Let's consider the product 1.2.3.4.5.6.7.8.9.10.11.12.13. Since $2 \cdot 5=10$, and the product contains the factor 10, we get: $1 \cdot 3 \cdot 4 \cdot 6 \cdot 7 \cdot 8 \cdot 9 \cdot 11 \cdot 12 \cdot 13 \cdot 100$ which means the last two digits of the product are zeros.

## V section