Is the product of 2002 continuous natural numbers odd or even? Why

As long as there are two continuous natural numbers, one of them must be even. So the product must be a multiple of 2
The product of three continuous natural numbers must be a multiple of 6;
The product of four continuous natural numbers must be a multiple of 24;
The product of five continuous natural numbers must be a multiple of 120;
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RELATED INFORMATIONS

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9. If the sum of two natural numbers is 50 and their greatest common divisor is 5, then there are () groups of numbers satisfying the condition
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12. Is the product of 202 continuous natural numbers odd or even?
13. Is the product of 30 continuous natural numbers odd or even?
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19. A number minus 100 is a square number, minus 63 is also a square number, how much is this?
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