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Answered 2012-09-25 05:55:56

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

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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.


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.



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.


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.


If sum of two consecutive integers is 228 find the integers?

The sum of any two consecutive integers must be an odd number. So this question is incorrect.


What is the least common multiple of 20 and 21?

The LCM of 20 and 21 is 420. The LCM of any pair of consecutive integers is their product.


Use pigeonhole principle to show that one of any n consecutive integers divisible by n?

Let's look at a simple example first such as 3 consecutive integers. We want to show that it is divisible by 3.Take 4,5, and 6 and of course 6 is divisible by 3.The reason for this is can be seen using the pigeonhole principle.When an integer is divided by 3, possible remainders are 0, 1, and 2. It follows that everyinteger can be expressed in one of the forms 3k, 3k + 1, and 3k + 2 where k is an integer.So if we have any three consecutive integers, one of them must be divisible by 3.Let's look at how the pigeonhole principle applies. Suppose we have 3 consecutive integers are non are divisible by 3. Think of the pigeon holes as 3k, 3k + 1, and 3k + 2, now this means no numbers are in the 3k hole and two of them must be in either the 3k+1 hole or the 3k+2 hole. But this contradicts that they are consecutive integers.So for any n, let the pigeon holes be nk, nk+1,... nk+(n-1) and these exhaust the multiples of n. Now if you take n consecutive numbers, you must have a least 1 number in the nk pigeon hole or else they are not consecutive.


A pair of consecutive co prime numbers?

Any pair of consecutive integers is co-prime.


Show consecutive odd numbers divisible by 4?

There aren't any odd numbers divisible by 4, much less consecutive ones.


What two consecutive integers does 138 lie between?

138 is, itself, an integer. It is impossible for any integer to lie between two consecutive integers.


What is a consecutive composite number?

It's any set of consecutive integers that are composite. For instance, 8, 9, and 10 are consecutive composites.


Is the sum of any consecutive integers even?

The sum of any two consecutive integers is odd. Try it out. 3 + 4 = 7 4 + 5 = 9 If it works for those, it works for all of them.



Is the product of any two integers an integer?

Yes, the product of 2 integers are always an integers. ex. -2*3=-6




What are four consecutive numbers that add up to 268?

There are no such numbers. If S is the sum of any 4 consecutive integers then S = 2 (mod 4) In other words, any four consecutive integers add up to an even number that is NOT dvisible by 4.


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