Question

What is the GCF of \[18a,20ab\] and \[6ab\]?

Answer 1

Hint: Here, we have to use the concept of the factorization and HCF Factorization is the process in which a number is written in the forms of its small factors which on multiplication give the original number, we will factorize both the numbers separately. After the factorization we will take maximum common factors of the three numbers to get the value of the HCF or GCF. HCF or Highest, Common Factor is the largest factor which is the common divisor among the numbers

Complete step-by-step answer:
Given numbers are \[18a,20ab\] and \[6ab\]
First, we have to find out the factors of the given numbers. Factors are the smallest numbers with which the given number is divisible and their multiplication will give the original number
So, factors of the number \[18a\] are \[18a=2\times 3\times 3\times a\]
Similarly, we will find the factors of the other number \[20ab\]
Factors of the number \[20ab\] are \[20ab=2\times 2\times 5\times a\times b\]
Similarly, we will find the factors of the other number \[6ab\]
Factors of the number \[6ab\] are \[6ab=2\times 3\times a\times b\]
Now, to find out the HCF of the numbers we will take maximum common factors among all the numbers i.e., factor \[2\] and \[a\] which occurs common in all the three numbers. Therefore, we get HCF of the numbers is equal to \[2\times 3\]
Therefore, the HCF of the numbers \[18a,20ab\] and \[6ab\] is equal to $2\times a=2a$

Note: We know that HCF of the numbers is generally less than or equal to the LCM of the number. LCM is the lowest common factor which is exactly divisible by both the numbers, in other words, it is the smallest number which is the multiple of the numbers. Product of LCM and the HCF of original numbers are equal to the product of the original numbers