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Question
The number of common prime factors of 75, 60, 105 is ______.
Options
2
3
4
5
MCQ
Fill in the Blanks
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Solution
The number of common prime factors of 75, 60, 105 is 2.
Explanation:
We have,
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
| 2 | 60 |
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
75 = 3 × 5 × 5
60 = 2 × 2 × 3 × 5
105 = 3 × 5 × 7
∴ The common prime factors of 75, 60 and 105 are 3 and 5 i.e., 2 in number.
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