Question

What is the highest common factor of \[11\] and \[5\] ?

Answer 1

Hint: In this type of question, we have to use the concept of H.C.F. When we try to find out the H.C.F. we have to first write all the factors of the given numbers. Then we have to consider all the common factors of the given numbers. Now from the common factors, we have to find out the highest common factor. In this way, we can find out the highest common factor of the given numbers.

Complete step-by-step answer:
We have given the numbers as \[11\] and \[5\]
And we have to find the highest common factor of \[11\] and \[5\]
Now let us consider all the possible factors of \[11\] and \[5\] which are as follows:
Factors of \[11\] : \[11 \times 1\]
Factors of \[5\] : \[5 \times 1\]
Now we have to find out all the common factors of \[11\] and \[5\]
Here, we can observe that the common factors of \[11\] and \[5\] is \[1\]
Hence, the common factor i.e., H.C.F. of \[11\] and \[5\] is \[1\]

Note: Here we can also use the concept that both \[11\] and \[5\] are prime numbers i.e., they only have themselves and \[1\] as factors. Hence, the only common factor they have is \[1\] which is also the highest common factor.
Also, in this type of questions, students need to remember that the H.C.F. has to be only one number because it is the highest common factor of all the given numbers. Also, students have to take care that they don't mix up H.C.F. with L.C.M. As H.C.F stands for highest common factors while L.C.M. stands for least common multiple.