A cuboid of dimensions 50 cm, 150 cm, 175 cm can be divided into how many identical largest cubes?

Dimensions of the cuboid: 50 cm, 150 cm, and 175 cm.

To divide the cuboid into the largest possible identical cubes, we need to find the side length of the largest cube that can fit into the cuboid. The side length of the largest cube will be the greatest common divisor (GCD) of the three dimensions of the cuboid.

GCD (Greatest Common Divisor) of the dimensions.

Number of cubes = $$\frac{\text{Volume of the cuboid}}{\text{Volume of one cube}}$$​​

the GCD of the dimensions (50, 150, and 175).

Prime factorization of 50 = $$2 \times 5^2$$​​

Prime factorization of 150 = $$2 \times 3 \times 5^2$$​​

Prime factorization of 175 = $$5^2 \times 7$$​​

The GCD of 50, 150, and 175 is =$$5^2$$​ = 25 cm.

Thus, the side length of the largest cube is 25 cm.

Number of cubes:

$$\text{Number of cubes} = \frac{ 50 \times 150 \times 175}{25 \times 25 \times 25 }$$​ = 84

Thus, the cuboid can be divided into 84 identical cubes.