4. The product of the ages of the four members of a family is 36,260. How old are the members of this family if it is known that the father is two years older than the mother, and the daughter is three years younger than the son?
4. The number 36260 is factored into prime factors:
$36260=2 \cdot 2 \cdot 5 \cdot 7 \cdot 7 \cdot 37$ ..... 2 POINTS
Since the father is the oldest, we conclude that he could be 37 years old. ..... 1 POINT
In this case, the mother would be $37-2=35$ years old, and $35=5 \cdot 7$. ..... 1 POINT
By grouping the remaining prime factors, we get
$36260=37 \cdot(5 \cdot 7) \cdot(2 \cdot 2) \cdot 7=37 \cdot 35 \cdot 4 \cdot 7$ ..... 1 POINT
and we conclude that the son could be 7 years old, and the daughter $7-3=4$ years old $(\text{and } 4=2 \cdot 2$ ).
The father is 37 years old, the mother is 35, the son is 7, and the daughter is 4 years old.
1 POINT
TOTAL 6 POINTS

Note: The student is expected to explain the method of grouping, i.e., justify why the factors are grouped in this particular way. A correct result without the appropriate justification is scored 4 points.