Question
Download Solution PDFIf n is a natural number, then (6n2 + 6n) is always divisible by:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The expression is 6n² + 6n, where n is a natural number.
Formula used:
Factorize the expression to check for divisibility:
6n² + 6n = 6n(n + 1)
Calculations:
The expression 6n(n + 1) represents the product of 6, n, and (n + 1). Since n and (n + 1) are two consecutive integers, one of them will always be divisible by 2, making their product divisible by 2. Additionally, the 6 in the expression ensures that the entire product is divisible by 6.
∴ 6n² + 6n is always divisible by 6.
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