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The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer?
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The product of three consecutive positive integers is divisible by 6 i...
It's true because consecutive means accordingly or we can say that number wise .let one of the no.be 1then it's two consecutive no is 2and 3 respectively and if we multiply these numbers we get 6 as a result.
Community Answer
The product of three consecutive positive integers is divisible by 6 i...
Answer:
The statement is true.
Explanation:
We know that 6 is the product of 2 and 3. Therefore, if a product of three consecutive positive integers is divisible by 6, it must be divisible by both 2 and 3.
Let's consider three consecutive positive integers: x, x+1, and x+2.
The product of these three integers is:
x(x+1)(x+2)
To determine if this product is divisible by 6, we need to check if it is divisible by both 2 and 3.
Divisibility by 2:
One of the three consecutive integers must be even (i.e. divisible by 2), and the other two must be odd. Therefore, the product of any three consecutive integers must be divisible by 2.
Divisibility by 3:
To determine if the product is divisible by 3, we can use the fact that the sum of the digits of any multiple of 3 is also a multiple of 3.
x + (x+1) + (x+2) = 3x + 3
This expression is clearly divisible by 3, and therefore the product x(x+1)(x+2) is also divisible by 3.
Since the product is divisible by both 2 and 3, it must be divisible by 6.
Therefore, the statement "the product of three consecutive positive integers is divisible by 6" is true.
The statement is true.
Explanation:
We know that 6 is the product of 2 and 3. Therefore, if a product of three consecutive positive integers is divisible by 6, it must be divisible by both 2 and 3.
Let's consider three consecutive positive integers: x, x+1, and x+2.
The product of these three integers is:
x(x+1)(x+2)
To determine if this product is divisible by 6, we need to check if it is divisible by both 2 and 3.
Divisibility by 2:
One of the three consecutive integers must be even (i.e. divisible by 2), and the other two must be odd. Therefore, the product of any three consecutive integers must be divisible by 2.
Divisibility by 3:
To determine if the product is divisible by 3, we can use the fact that the sum of the digits of any multiple of 3 is also a multiple of 3.
x + (x+1) + (x+2) = 3x + 3
This expression is clearly divisible by 3, and therefore the product x(x+1)(x+2) is also divisible by 3.
Since the product is divisible by both 2 and 3, it must be divisible by 6.
Therefore, the statement "the product of three consecutive positive integers is divisible by 6" is true.
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The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer?
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The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer?.
The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of three consecutive positive integers is divisible by 6 is this statement teue or false?justify your answer?.
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