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Is the sum of any three consecutive counting numbers always divisible by 3?
Wiki User
∙ 9y ago
Yes.
Choose any three consecutive counting numbers.
The first number is the second number subtract 1
The third number is the second number add 1
Adding the three numbers together is the same as adding:
(the second number subtract one) plus the second number plus (the second number add one).
The "subtract one" and "add one" cancel each other out to leave the sum as:
the second number plus the second number plus the second number
Which is the same as 3 times the second number, ie the sum is a multiple of 3 and so is divisible by 3.
For example:
10 + 11 + 12 = (11 - 1) + 11 + (11 + 1) = 11 - 1 + 11 + 11 + 1 = 11 + 11 + 11 + (1 - 1) = 11 + 11 + 11 + 0 = 11 + 11 + 11 = 3 x 11
Wiki User
∙ 9y ago
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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.
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
Why can't two consecutive whole numbers be prime?
In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.
How do you make 92 with consecutive numbers?
Adding consecutive pairs of numbers will always turn out to be an odd number. It would have to be consecutive odd numbers: 45 and 47.
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
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.
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
Are whole numbers always a counting numbers?
No. 0 and negative integers are whole numbers but they are not counting numbers.
Are counting numbers always whole numbers?
Whole numbers include the number 0 and counting numbers do not.
Why can't two consecutive whole numbers be prime?
In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.
Why 35 and 7 are the only three consecutive odd prime numbers?
If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.
Why arent there any other consecutive prime numbers besides 2 and 3?
Because any consecutive pair of numbers would involve an even number which will always be divisible by 2. As 2 is the only even prime number, 2 and 3 are necessarily the only sequential prime numbers.
How do you make 92 with consecutive numbers?
Adding consecutive pairs of numbers will always turn out to be an odd number. It would have to be consecutive odd numbers: 45 and 47.
What any two consecutive numbers add up to make 12?
Consecutive numbers will always total an odd number. Consecutive odd numbers or consecutive primes would be 5 and 7.
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 always the sum of three consecutive whole numbers?
The sum of 3 consecutive whole numbers is always equal to 3 times the middle number in that sequence.
Show that 5 always divides evenly into the sum of any five consecutive counting numbers?
Chose any integer x. Five consecutive numbers: x, x+1, x+2, x+3, x+4 The sum of these numbers is 5x+10. Factoring: 5(x+2) You can always divide this evenly by 5, giving x+2.
