To find the total amount of the cash prize that Noam must share among 4 winners, we can multiply the amount each person receives by the number of winners.
Each person receives $125, and there are 4 winners:
\[ \text{Total Amount} = \text{Amount per person} \times \text{Number of winners} = 125 \times 4 = 500 \]
Thus, the total amount of the prize is $500.