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If you are multiplying negative numbers, an odd number of factors will have a negative product. An even number of factors will have a positive product.
As a product of its prime factors: 3*3*5*5*7*7 = 11025
No, only the number of negative factors affect its sign.
21 as a product of its prime factors is 1 X 3 X 7.
As a product of its prime factors: 2*2*2*5*7 = 280