To determine which of the given numbers is divisible by 47, we need to check each number by dividing it by 47 and seeing if the remainder is 0.

Checking Divisibility by 47

There isn't a simple shortcut rule for checking divisibility by 47. The most reliable method is direct division.

Option 1: Checking 3674

Let's divide 3674 by 47:

$$ \frac{3674}{47} $$

Performing the division:

$$ 3674 \div 47 \approx 78.17 $$

Since the result is not a whole number, 3674 is not divisible by 47.

Option 2: Checking 4416

Let's divide 4416 by 47:

$$ \frac{4416}{47} $$

Performing the division:

$$ 4416 \div 47 \approx 93.96 $$

As the result is not a whole number, 4416 is not divisible by 47.

Option 3: Checking 3995

Let's divide 3995 by 47:

$$ \frac{3995}{47} $$

Performing the division:

$$ 3995 \div 47 = 85 $$

The result is a whole number (85), which means 3995 is perfectly divisible by 47.

Option 4: Checking 3816

Let's divide 3816 by 47:

$$ \frac{3816}{47} $$

Performing the division:

$$ 3816 \div 47 \approx 81.19 $$

Since the result is not a whole number, 3816 is not divisible by 47.

Conclusion

Based on the division checks, the number 3995 is the only number among the options that is exactly divisible by 47.