# The dimensions of a rectangular parallelepiped are expressed in prime numbers. its volume is

**The dimensions of a rectangular parallelepiped are expressed in prime numbers. its volume is 1) 66 cm3. 2) 195 cm3. 3) 255 cm3. What are the dimensions of a rectangular parallelepiped?**

Let’s denote the measurements of this rectangular parallelepiped through x1, x2 and x3.

The volume V of a rectangular parallelepiped can be determined in the formula:

V = x1 * x2 * x3.

According to the condition of the problem, the measurements of a given rectangular parallelepiped are expressed in prime numbers.

Therefore, in order to find the dimensions of a given rectangular parallelepiped, you need to decompose the number V into the product of three prime factors.

1)

V = 66 cm³.

66 = 11 * 6 = 11 * 3 * 2.

Therefore, the measurements of this rectangular parallelepiped are 11 cm, 3 cm and 2 cm.

2)

V = 195 cm³.

195 = 5 * 49 = 5 * 7 * 7.

Therefore, the measurements of this rectangular parallelepiped are 5 cm, 7 cm and 7 cm.

3)

V = 255 cm³.

255 = 5 * 51 = 5 * 3 * 17.

Therefore, the measurements of this rectangular parallelepiped are 5 cm, 3 cm and 17 cm.