Question

What are the common factors for the numbers \[6{\text{ and 15}}\]?

Answer 1

Hint: Factors of a given number are the numbers by which if we divide the given number then, the remainder will be zero. In the question we are asked to find the common factors of the two given numbers. So, for that we will first list the factors of each number and then choose the common factors from them.

Complete step by step answer:
We will first write the factors of each number. So, factors of:
\[6 = 1,2,3,6\]
\[15 = 1,3,5,15\]
We can see that the common factors are \[1,3\].

Additional details:
If in the question we were asked to find the greatest common factor then we would have chosen the greatest number common in their factors i.e., \[3\]. If a number has only two factors i.e., one and the number itself then, that given number is called the prime number. If two numbers have only \[1\] as their common factor, then those numbers are called co-prime numbers.

Note:
One important point to note is that there is a difference between the factors and multiples of a number. Factors are the numbers by which the given number is completely divisible. Multiples of a number are the numbers which are completely divisible by the given number. Factors are always less than or equal to the given number whereas multiples are either equal or greater than the given number. In case of the polynomials, the factors have degrees less than or equal to the given polynomial. Another interesting thing is that we cannot find the greatest multiple of a number.