Question

Find the HCF of the following numbers: 510 and 92.

Answer 1

Hint: First of all, try to recollect the meaning of HCF that is the highest common factor of numbers. Now prime factorize the number individually and find the factors common to all three.

Complete step-by-step solution -
Here, we have to find the HCF of 510 and 92. Before proceeding with the question, let us first see what HCF is. HCF is the highest common factor between the numbers. In other words, we can say that HCF is the longest or the greatest factor common to any two or more given natural numbers.
For example, HCF of 5, 10, and 15. Here,
\[\begin{align}
  & 5=5\times 1 \\
 & 10=5\times 2 \\
 & 15=5\times 3 \\
\end{align}\]
Here, HCF of 5, 10, and 15 is 5.
Now, let us consider our question. First of all, let us perform the prime factorization of 510, we get,

So, we get,
\[510=2\times 3\times 5\times 17.....\left( i \right)\]
Now, let us perform the prime factorization of 92, we get,

So, we get,
\[92=2\times 2\times 23.....\left( ii \right)\]
From equation (i) and (ii), we get,
\[510=2\times 3\times 5\times 17\]
\[92=2\times 2\times 23\]
From the above two equations, we can see that the common factor of 510 and 92 is just 2. So, we get the highest common factor or HCF of 510 and 92 as 2.

Note: In this question, students often make this mistake of leaving one or the other factor which is common to all three numbers. So, first of all, they should properly point out the numbers common to all the three and then only give the final answer. Also, note that dividing prime factorization of numbers takes each prime factor of the given number starting from the smallest prime number.