Question

Find common factors of 2, 6 and 8.

Answer 1

Hint: There are two methods to factorize a number one by division method, where the number is divided by the prime number to get the smallest number. Another method is the factor tree, where the number is broken down into factors to get the smallest number. Here, the question is asking for the HCF of the numbers 1836, 810, 1296, and 702, so the first step will be to factorize the numbers and then multiply the common unique numbers among the factors of all numbers. The factors are the integers, which, when multiplied, results in the number itself.
To find common factors of 2, 6 and 8 we have to find the L.C.M of a number and thus we can easily find the common factors by prime factorization.


Complete step by step solution:
First find all the factors of 2, 6 and 8 as:
$$\begin{gathered} 2=2\times 1 \\ 6=2\times 3\times 1 \\ 8=2\times 2\times 2\times 1 \end{gathered}$$

Now check occurrence of numbers in each case:
Factors of 2 includes 1 (one time) and 2 (one time)
Factors of 6 includes 1 (one time), 2 (one time) and 3 (one time)
Factors of 8 includes 1 (one time) and 2 (three times)

Now, we can see that the common factors for the numbers 2, 3 and 6 are 1 and 2 only.
So, common factors which are included in all these (2, 6, 8) are 1 and 2.


Note: In this question, it is very easy to calculate the factors of numbers either by prime factorization or by ladder method whichever is convenient.