Question 7

How many divisors other than 1 and 7200 does 7200 have?

Solution

7200 has to be prime factorized :
7200 = 6 x 1200
= 6 x 6 x 200
= 2 x 3 x 2 x 3 x 2 x 2 x 5 x 2 x 5
= $$2^5\times3^2\times5^2$$

Total No of factors = (5+1)(2+1)(2+1) = 6 x 3 x 3 = 54 factors .

So, No of proper divisors are (54 - 2) = 52 . { Out of 54 factors, we need to subtract 1 & 7200 }

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