Question

The number of divisors of 8400 except unity is
1)58
2)59
3)60
4)61​

Answer 1

Answer:

3)60

Step-by-step explanation:

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Answer 2

Answer:

58

Step-by-step explanation:

8400=4×100×21=18×25×3×7

=3 ^1.2^4.5^2.7 ^1

=3^a.2^b.5^c 7^d

a varies from 0 to 1, b from 0 to 4, c from 0 to 2 and d again from 0 to 1.

Thus the total number of divisors is

= 2×5×3×2=60

We have to exclude the divisor 1 and the divisor 8400. i.e. the number itself. Hence required number is 60−2=58.

Sum of the divisors

Any divisor is of the form 3^a2^b5^c7^d

Sum = ∑ 1,0 3^a ∑ 4,0 2^b ∑2,0 5^c ∑ 1,0 7^d

=(1+3)(1+2+2^2+2^3+2^4)(1+5+5^2)(1+7)

=4×31×31×8.