What is the digit in the units place of the product 51 × 52 × 53 × ... × 59?

Introduction / Context:
This question tests your ability to find the units digit of a large product without actually multiplying all the numbers. The key idea is to focus only on the units digits and to use the fact that a factor of 10 guarantees a units digit of 0 in the product.

Given Data / Assumptions:

- The product is 51 × 52 × 53 × ... × 59.

- These are 9 consecutive integers from 51 up to 59.

- We are only interested in the units digit of this product.

Concept / Approach:
If the product of several integers contains at least one factor 2 and one factor 5, then the product will be divisible by 10 and the units digit will be 0. In a longer product of consecutive integers, it is almost certain that both factors 2 and 5 appear, and often an entire factor of 10 appears directly.

Step-by-Step Solution:
Step 1: Look for numbers ending in 0 or 5 in the product. Among 51, 52, 53, 54, 55, 56, 57, 58, 59, the only number ending in 5 is 55. Step 2: Check for even numbers. We have many even numbers: 52, 54, 56, 58 are all even. Step 3: Note that 55 provides a factor 5 and any even number provides a factor 2. So, the product contains at least one factor 2 * 5 = 10. Step 4: Once there is a factor 10 in the product, the units digit of the entire product must be 0.

Verification / Alternative check:
You can also notice that 55 × 52 already ends with 0 because 55 × 52 = (5 × 11) × (4 × 13) and clearly includes 5 × 2 = 10. Multiplying further by any other integers will keep the units digit 0 because 10 times any integer ends with 0.

Why Other Options Are Wrong:
- 4, 3, 6: These digits arise in units digits of some smaller products, but once a full factor of 10 is present, the units digit cannot be anything other than 0.

Common Pitfalls:
Some students try to compute the entire product or track every multiplication, which is time consuming and error prone. Others look only at the first and last numbers instead of checking for factors 2 and 5. Remember that the appearance of 2 and 5 together is enough to fix the units digit as 0.

Final Answer:
The units digit of the product 51 × 52 × 53 × ... × 59 is 0.