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Why is the product of 3 consecutive integers always divisible by 6?
Wiki User
∙ 11y ago
Let the three integers be, n, (n + 1), and (n + 2)
Then at least one of these numbers is even and therefore has a factor of 2.
And one of the numbers is divisible by 3 **.
Therefore the product has factors of 2 and 3 and is thus divisible by 2 x 3 = 6.
** Either n is divisible by 3.
Or, n leaves a remainder of 1 when divided by 3 in which case (n + 2) is divisible by 3.
Or, n leaves a remainder of 2 when divided by 3 in which case (n + 1) is divisible by 3.
Wiki User
∙ 11y ago
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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
Two consecutive negative integers have a product of 240 what are the integers?
First, we are not interested for the sign of the numbers, because the product of two negative numbers is always positive, so we need to find the two consecutive factors of 240, which are 15 and 16. Thus, the numbers are -16 and -15.
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.
Is the product of two negative integers always negative?
That is false. The product of two negative integers is always positive.
Will the sum of 6 consecutive numbers always be divisble by 3?
If you mean six consecutive INTEGERS, then the answer is Yes.
Sum of three consecutive integers is divisible by three?
yes always this is true' example 1,2,3 sum is 6 and is divisible by 3
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
Will the product of two consecutive integers be odd or even?
It will alway be even, because it will always be the product of an odd and an even number, which is always even.
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
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.
What are consecutive integers with the sum of 116?
The sum of two consecutive integers will always be an odd number.
Two consecutive negative integers have a product of 240 what are the integers?
First, we are not interested for the sign of the numbers, because the product of two negative numbers is always positive, so we need to find the two consecutive factors of 240, which are 15 and 16. Thus, the numbers are -16 and -15.
Is the sum of two consecutive numbers always divisible by 2?
No, the sum of two consecutive numbers is always an odd number, and is not divisible by two.
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.
Is the product of two negative integers always negative?
That is false. The product of two negative integers is always positive.
What three consecutive numbers add up to 25?
That isn't possible. The three consecutive number are assumed to be integers; the sum of three consecutive integers is always a multiple of 3 (try it out).
Will the sum of 6 consecutive numbers always be divisble by 3?
If you mean six consecutive INTEGERS, then the answer is Yes.
