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Find the highest power of 24 in 150!

  • a)
    46

  • b)
    47

  • c)
    48

  • d)
    49

Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Find the highest power of 24 in 150!a)46b)47c)48d)49Correct answer is ...
24 = 8 × 3
Therefore, we need to find the highest power of 8 and 3 in 150!
8 = 23
Highest power of 8 in 150! is:
= [(150 / 2) + (150 / 4) + (150 / 8) + (150 / 16) + (150 / 32) + (150 / 64) +(150 / 128)] / 3
= 48
Highest power of 3 in 150! is:
= [150 / 3] + [150 / 9] + [150 / 27] + [150 / 81]
= 72
As the powers of 8 are less, powers of 24 in 150! = 48
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Find the highest power of 24 in 150!a)46b)47c)48d)49Correct answer is ...
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Find the highest power of 24 in 150!a)46b)47c)48d)49Correct answer is option 'C'. Can you explain this answer?
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