Let the two whole numbers be \( x \) and \( y \).
According to the problem, we have two equations:
- \( x \cdot y = 147 \) (their product)
- \( \frac{x}{y} = 3 \) (their quotient)
From the second equation, we can express \( x \) in terms of \( y \):
\[ x = 3y \]
Now, we can substitute this expression for \( x \) into the first equation:
\[ (3y) \cdot y = 147 \]
This simplifies to:
\[ 3y^2 = 147 \]
Next, divide both sides by 3:
\[ y^2 = 49 \]
Taking the square root of both sides, we find:
\[ y = 7 \]
Now, substitute \( y \) back into the expression for \( x \):
\[ x = 3y = 3 \cdot 7 = 21 \]
Thus, the two whole numbers are \( x = 21 \) and \( y = 7 \).
To verify:
- Their product: \( 21 \cdot 7 = 147 \) (correct)
- Their quotient: \( \frac{21}{7} = 3 \) (correct)
Therefore, the two whole numbers are 21 and 7.