Question

Write the condition under which the hcf of the given algebraic expression is 1​

Answer 1

Answer:

A HCF is the highest common factor between 2 or more numbers. because every number times 1 is equal to itself, every 2 numbers have a common factor of 1.

HCF between 2 numbers a,b or expressions such that a and b are not equal to 0 , will never be 0 , because of the simple fact that anything times 0 is equal to 0 , and we stated that a,b isn’t equal to 0 , so that’s a contradiction.

Since you stated that there is no common factor bigger or lower than 1 between the 2 numbers (which means that the two numbers are equal to each other and equal to 1 or 0 , think about it yourself a little bit) that means that the only factor is 1 when the two numbers are not 1 , and 0 or anything if the two numbers are 0 , because again, every number times 0 is equal to 0 .

So finally, there is not HCF if the two numbers stated are both 0 , and the only other possibility is for them to be 1 , and in this case, the HCF will be 1 .