Question

What is the greatest common factor of 21 and 63?

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 both the numbers to get the value of the HCF. HCF or Highest, Common Factor is the largest factor which is the common divisor of both the numbers

Complete step-by-step solution:
Given numbers are 21, 63.
First, we have to find out the factors of the given numbers i.e., 21,63. 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 21 are $3\times 7$
Similarly, we will find the factors of the other number 63
Factors of the number 63 are $3\times 3\times 7$
Now, to find out the HCF of the numbers we will take maximum common factors of both the numbers i.e., factor 3 and 7 which occurs one time in number 21 and 63. Therefore, we get HCF of the numbers 21, 63 is equal to $3\times 7$.
HCF of the numbers 21, 63 is equal to $3\times 7=21$
Hence, the HCF of the given numbers i.e., 21 and 63 is $21$.

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