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How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?
[2019]
- a)42
- b)43
- c)44
- d)45
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
How many factors of 24 × 35 × 104 are perfect squares whic...
24 × 35 × 104 = 28 × 35 × 54
For perfect squares, we have to take only even powers of the prime factors of the number
The number of ways 2’s can be used is 5 i.e. 20, 22, 24, 26, 28
The number of ways 3’s can be used is 3 i.e. 30, 32, 34
The number of ways 5’s can be used is 3 i.e. 50, 52, 54
Therefore, the total number of factors which are perfect squares = 5 × 3 × 3 = 45
But this also includes the number 1.
Hence excluding 1, the required number is 45 – 1 = 44.
For perfect squares, we have to take only even powers of the prime factors of the number
The number of ways 2’s can be used is 5 i.e. 20, 22, 24, 26, 28
The number of ways 3’s can be used is 3 i.e. 30, 32, 34
The number of ways 5’s can be used is 3 i.e. 50, 52, 54
Therefore, the total number of factors which are perfect squares = 5 × 3 × 3 = 45
But this also includes the number 1.
Hence excluding 1, the required number is 45 – 1 = 44.
Most Upvoted Answer
How many factors of 24 × 35 × 104 are perfect squares whic...
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, there are 8 factors of 24.
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How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?[2019]a)42b)43c)44d)45Correct answer is option 'C'. Can you explain this answer?
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How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?[2019]a)42b)43c)44d)45Correct answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?[2019]a)42b)43c)44d)45Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?[2019]a)42b)43c)44d)45Correct answer is option 'C'. Can you explain this answer?.
How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?[2019]a)42b)43c)44d)45Correct answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?[2019]a)42b)43c)44d)45Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?[2019]a)42b)43c)44d)45Correct answer is option 'C'. Can you explain this answer?.
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