Question

Find the HCF of 250 and 30.

Answer 1

Hint: In this question, the first thing that we should do is to write each number as a product of its prime factors. This method is called here prime factorization. Now list the common factors of both the numbers. The product of all common prime factors is the HCF (use the lower power of each common factor).

Complete step-by-step answer:
In this question, we have two numbers 250 and 30.
Now, write each number as a product of its prime factors.
Example: prime factors of 15 are 3 and 5.
$250 = 2 \times 5 \times 5 \times 5$
In this case prime factors of 250 are 2 and 5.
$30 = 2 \times 3 \times 5$
In this case prime factors of 30 are 2, 3 and 5.
As we know, the products of all common prime factors are the HCF (use the lower power of each common factor).
The common prime factors in this example are 2 and 5.
The lowest power of 2 is 2 and 5 is 5.
So, $HCF=2 \times 5$
              =$10$
Therefore, we can write:
HCF of 250 and 30 is 10.

Note: This type of question can be solved in two ways. First is the prime factorization method. Here we find the prime factors of the given numbers and then find the product of the common factors to get the HCF. Second method is the long division method. Here we first divide the two numbers then the remainder that comes becomes divisor and the earlier divisor becomes dividend. Repeat this step till the remainder becomes zero. The final divisor will give the HCF.