Question

Find HCF of 650 and 1170 .

Answer 1

Hint: Here, we are required to find the H.C.F of the given two numbers. We will find the factors of the two numbers by using the prime factorization method. We will select the factors which are common in both the numbers will give us the required (H.C.F) of the two numbers.

Complete step by step answer:
A Highest common factor (H.C.F) is the greatest number that is a factor of two or more numbers. This is also known as the Greatest Common Factor (G.C.F).
We have to find the H.C.F of two numbers.
By using the prime factorization method, we will find the factor of the given two numbers.
We will now factorize 650.
We can see that 650 is an even number, so we will divide it by least prime number 2. Therefore, we get
\[650\div 2=325\]
Now dividing 325 by 5, we get
\[325\div 5=65\]
Now dividing 65 by 5, we get
\[65\div 5=13\]
Now as we have got the prime number as the quotient, so we will divide it further.
\[650=2\times 5\times 5\times 13\]
Now we will factorize 1170, we get
We can see that 1170 is an even number, so we will divide it by least prime number 2. Therefore, we get
\[1170\div 2=585\]
Now dividing 585 by 5, we get
\[585\div 5=117\]
Now dividing 117 by 3, we get
\[117\div 3=39\]
Now dividing 39 by 3, we get
 \[39\div 3=13\]
Now we have got the prime number as the quotient, so we will not divide further.
Hence, 1170 can be written as:
\[1170=2\times 3\times 3\times 5\times 13\]
Now, as we can see, the common factor in both the number is 2, 5 and 13.
\[HCF=2\times 5\times 13=130\]

Therefore, H.C.F of 650 and 1170 is 130.

Note: In order to find HCF of two numbers it is really important to express those numbers as a product of their prime factors. Prime factors are those factors which are greater than 1 and gave only two factors, i.e., factor 1 and the number itself.