How many more positive divisors does 6000 has as compared to 2100 ?

The answer is 4.

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$6000 = 2^4 \cdot 3 \cdot 5^3 \\ 2100 = 2^2 \cdot 3 \cdot 7 \cdot 5^2$

Using the number of factor theorem , number of factors of 6000 are $5 \cdot 2 \cdot 4 = 40$ and the number of factors of 2100 are $2 \cdot 2 \cdot 3 \cdot 3 = 36$ .

Therefore, 6000 has $40 - 36 = 4$ factors more than 2100.