Table of Contents
What is the product of 3 consecutive numbers?
If n = 3k + 2, then n + 1 = 3k + 2 + 1 = 3k + 3 = 3(k + 1) which is again divisible by 3. So we can say that one of the numbers among (n, n + 1 and n + 2) is always divisible by 3. Therefore the product of numbers n(n+1)(n+2) is always divisible by 3.
Why is the product of 3 consecutive numbers always divisible by 6?
For example if you had your three numbers as: 5, 6, 7, one is divisible by 3 and one is divisible by 2, as this is the case with all consecutive three numbers. Therefore as we are multiplying the numbers together, multiplying a multiple of 3 and a multiple of 2 gives us a multiple of 6.
Can consecutive numbers be divided by 3?
Your 4 Page 5 first theorem showed that the sum of two consecutive numbers is odd. In other words, the sum of 2 consecutive numbers is not divisible by 2. The second theorem showed that the sum of 3 consecutive numbers is divisible by 3.
How do you prove three consecutive numbers are divisible by 6?
So, we can say that one of the numbers among n,n+1 and n+2 is always divisible by 3 that is:
- n(n+1)(n+2) is divisible by 3.
- Since, n(n+1)(n+2) is divisible by 2 and 3.
- Hence, n(n+1)(n+2) is divisible by 6.
Why the product of any three consecutive non zero whole numbers is divisible by 6?
Just like the investigation on sum of consecutive numbers we can start by using three consecutive numbers and multiplying them. The answers 6, 24, 60 are all divisible by 6, because each product has an even number and a multiple of 3. Therefore, a number that is always a divisible by 2 and 3 will be divisible by 6.
Is the sum of every three consecutive numbers divisible by 3?
Proposition: The sum of any three consecutive integers is divisible by 3. ANSWER: True. Since n+2 is an integer, 3(n+2) is divisible by 3.
What is the result when you square two consecutive numbers?
We noticed that the result is always even. This is always true, since, for any two consecutive numbers, one would be even and the other one odd. Since the square of an even number is even and the square of an odd number is odd, one of the squares of the two consecutive numbers will be even, and the other will be odd.
Can an even number of consecutive numbers add to make?
But if you add two consecutive numbers, the answer is always an odd number. So a sum like this must have an odd number as a factor again – but doesn’t. This proves that an even number of consecutive numbers cannot add to make .
What is the value of 3 consecutive numbers that equal 3?
If you add any 3 consecutive numbers together it will always equal a multiple of 3, e.g. 1+2+3=6 2+3+4=9 3+4+5=12
Are all odd numbers written as the sum of two consecutive numbers?
Many people spotted the pattern that all odd numbers (except 1) could be written as the sum of two consecutive numbers. For example, Matilda and Tamaris wrote: If you add two consecutive numbers together, the sum is an odd number, e.g. 1+2=3 2+3=5 3+4=7 4+5=9 5+6=11 6+7=13 and so on…