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

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To divide a cuboid into the largest possible identical cubes, we need to find the largest cube that can fit exactly into the cuboid. This is done by finding the Highest Common Factor (HCF) of the three dimensions.

Step 1: Find the HCF of 50, 150, and 175.

- 50 = 2 × 5 × 5
- 150 = 2 × 3 × 5 × 5
- 175 = 5 × 5 × 7

The common factor is 5 × 5 = 25.
So, the largest cube has a side of 25 cm.

Step 2: Find the number of such cubes in the cuboid:
- Number along 50 cm = 50 / 25 = 2
- Number along 150 cm = 150 / 25 = 6
- Number along 175 cm = 175 / 25 = 7

Total number of cubes = 2 × 6 × 7 = 84

Therefore, the cuboid can be divided into 84 identical largest cubes.

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