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What is the largest value of n such that 10n divides the product
25 × 33 × 48 × 43 × 67 × 76 × 812 × 99 × 106 × 1512 × 2014 × 2211 × 2515?
  • a)
    65
  • b)
    55
  • c)
    50
  • d)
    45
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the largest value of n such that 10n divides the product25 &ti...
For the number to be divisible by 10n , it must contain the same powers for 2 and 5
Power of 2 = 25+2.8+7+3.12+6+2.14 + 11 = 25+16+7+36+6+28+11 = 2109
Power of 5 = 53+6+12+14+2.15 = 565
Hence maximum possible power of 10 can be 65 only.
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Most Upvoted Answer
What is the largest value of n such that 10n divides the product25 &ti...
To find the largest value of n such that 10n divides the product 25, we need to find the prime factorization of 25.

The prime factorization of 25 is 5^2, because 5*5=25.

To divide 10n, we need to have at least two factors of 5. Since 5^2 has two factors of 5, the largest value of n such that 10n divides the product 25 is n=2.
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What is the largest value of n such that 10n divides the product25 × 33 × 48 × 43 × 67 × 76 × 812 × 99 × 106 × 1512 × 2014 × 2211 × 2515?a)65b)55c)50d)45Correct answer is option 'A'. Can you explain this answer?
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