We need to evaluate the expression: $51 \times 27 \times 35 \times 62 \times 75$ Simplify the Expression: Divide the expression by 100: $51 \times 27 \times 35 \times 62 \times 75 / 100$ ​

Simplify Further: Factor out $75 = 3 \times 25$:

$51 \times 27 \times 35 \times 62 \times \frac{3}{4}$ ​ Next, divide 62 by 2: $(51 \times 27 \times 35 \times 31 \times 3)/2$ ​ Check for Remainder when Divided by 2: Multiply the numbers: 51, 27, 35, 31, and 3—all of which are odd numbers.

The product of odd numbers is always odd. When an odd number is divided by 2, the remainder is 1. Account for Cancellation of 50: Since we factored out 50 earlier, the remainder must be multiplied by 50: $1 \times 50 = 50$

Final Answer: The remainder when $51 \times 27 \times 35 \times 62 \times 75$ is divided by 100 is 50.