Good luck listing all the factors

Number Theory Level 3

Which three-digit number has the greatest number of different factors?


The answer is 840.

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Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

Krishna Shankar
Jun 21, 2015

840 - It has 32 factors.

Factors for 840 are: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.

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How did you arrive at the conclusion that 32 is the maximum number of factors of a three digit number. Basically just telling you that your solution must be complete.

Kushagra Sahni - 5 years, 11 months ago

How do u know it is 840

Syed Hamza Khalid - 4 years, 1 month ago

2 3 5 7-primes-becomes 210, multiplying by 11 is too much, then multiply by 2 2=4, which has a greater number of factors than just 3. So you have (3+1)(1+1)(1+1)(1+1) = 32

Aloha Das - 2 years, 3 months ago

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