Tick true or false for the following statement. Give a reason for your answer. When 𝑛 is a positive integer, the value of 72𝑛 will always be divisible by eight.
The word “integer” means whole number. This means that the positive integers are one, two, three, four, and so on. In this question, 𝑛 must take one of these values. The number 72 is equal to eight multiplied by nine. This means that 72𝑛 can be written as eight multiplied by nine 𝑛.
We were asked to work out whether 72𝑛 will always be divisible by eight. Dividing 72𝑛 by eight is the same as dividing eight multiplied by nine 𝑛 by eight. Eight divided by eight is equal to one, as any number divided by itself equals one. This means that 72𝑛 divided by eight is equal to nine 𝑛.
As our value for 𝑛 is an integer, nine 𝑛 will also be an integer. Multiplying any whole number by nine gives us a whole number answer. We can therefore say that 72𝑛 is a multiple of eight and, as a result, must also be divisible by eight. The statement “When 𝑛 is a positive integer, the value of 72𝑛 will always be divisible by eight” is true.