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There must be three consecutive integers to guarantee that the product will be divisible by 6.

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

What are thress consecutive integers of 140?

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.


Explain why the product of any four consecutive integers is divisible by 24?

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.


Is the product of any 3 consecutive whole number is divisible by 6?

No.


What is the link between the product of any four consecutive positive integers and some square numbers?

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


What are two consecutive positive even integers of 340?

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.


What is the product of 15 consecutive integers whose average is7?

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.


If you take the 3 numbers in any consecutive trio and multiply them together to get a new number that new number will always be a multiple of 6 why is this?

18


The sum of 3 consective numbers is divisible by 3?

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


Does the product of any four consecutive whole number have any interesting properties?

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


Can you identify three consecutive even integers whose sum is 219?

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.


How many pairs of prime numbers are there which are consecutive odd integers?

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.


What is consecutive odd integers?

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

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