There are four students whose ages are just four consecutive natural numbers. The product of their ages is 5040. What is the sum of their ages?

There are four students whose ages are just four consecutive natural numbers. The product of their ages is 5040. What is the sum of their ages?

Solution: 5040 = 9x560 = 9x7x8x10
Therefore, the sum of their ages is: 7 + 8 + 9 + 10 = 34

Is the product of 2008 consecutive natural numbers odd or even? Why?
Come on,

Is an even number;
Because as long as there is an even number in it, the product is even
Even * odd = even
Even * even = even

Is the sum of any 2002 continuous natural numbers odd or even?

Because there are 1001 odd numbers and 1001 even numbers
So sum is even