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Q: Why is the product of any consecutive integers divisible by 6?

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Not sure what thress is. If three, then there is no answer since the sum (or product) of any three consecutive integers must be divisible by 3.

At least one of the four will be divisible by 4. One other will be divisible by 2 (but not by 4) One other will be divisible by 3. Hence the product will be divisible by 4 x 2 x 3 = 24.

No.

The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1

There aren't any. 340 is divisible by 4 while the sum of any two consecutive even numbers cannot be divisible by 4.There aren't any. 340 is divisible by 4 while the sum of any two consecutive even numbers cannot be divisible by 4.There aren't any. 340 is divisible by 4 while the sum of any two consecutive even numbers cannot be divisible by 4.There aren't any. 340 is divisible by 4 while the sum of any two consecutive even numbers cannot be divisible by 4.

I think the answer is zero. The only 15 consecutive integers whose average is 7 are the integers 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14. For any odd number of consecutive integers the average will be equal to the middle number, and this is the only group of 15 consecutive integers with 7 as the middle number. The product of any group of numbers that includes 0 will always be 0 because 0 times anything is 0.

18

Any three consecutive integers are divisible by three because it can be shown that the sum divided by three is the middle number.

It is always divisible by 24 and all the factors of 24.

No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.

There are an infinite number of prime numbers which are consecutive odd integers. Choose any natural number n. Take all primes up to any number n, take their product, and add 1 and subtract 1 from it. These 2 numbers are consecutive odd integers. eg 2*3*5*7 = 210 209 and 211 are primes which are consecutive odd integers.

For any integer n, the numbers 2n + 1 and 2n + 3 are consecutive odd integers.

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