Questions: Is 2 · 3 · 5 · 7 divisible by 5?

Transcript text: Is $2 \cdot 3 \cdot 5 \cdot 7$ divisible by 5 ?

Solution

Solution Steps

To determine if the product $2 \cdot 3 \cdot 5 \cdot 7$ is divisible by 5, we need to check if 5 is a factor of the product. Since 5 is one of the factors in the multiplication, the entire product is divisible by 5.

Step 1: Calculate the Product

We calculate the product of the numbers: \[ 2 \cdot 3 \cdot 5 \cdot 7 = 210 \]

Step 2: Check Divisibility by 5

To determine if $210$ is divisible by $5$, we check the condition: \[ 210 \mod 5 = 0 \] Since the remainder is $0$, $210$ is divisible by $5$.

Final Answer

The answer is A (Yes, because $5 \mid 5$). Thus, we conclude that the product is divisible by $5$.

\[ \boxed{\text{Yes, } 210 \text{ is divisible by } 5} \]

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