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Last updated date: 23rd Feb 2024
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Answer
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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. 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.).

Complete Step by Step Solution:
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 56.
We can see that 56 is an even number, so we will divide it by least prime number 2. Therefore, we get
\[56 \div 2 = 28\]
Now dividing 28 by 2, we get
\[28 \div 2 = 14\]
Now dividing 28 by 2, we get
\[14 \div 2 = 7\]
Now as we have got the prime number as the quotient, so we will not divide it further.
Hence, 56 can be written as:
\[56 = 2 \times 2 \times 2 \times 7\]
Now we will factorize 814, we get
We can see that 814 is an even number, so we will divide it by least prime number 2. Therefore, we get
\[814 \div 2 = 407\]
Now dividing 407 by the next least prime number 11, we get
\[407 \div 11 = 37\]
Now we have got the prime number as the quotient, so we will not divide it further.
Hence, 814 can be written as:
\[814 = 2 \times 11 \times 37\]
Now, as we can see, the common factor in both the numbers is only 2.

Therefore, H.C.F. of 56 and 814 is 2.

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 have only two factors, i.e. factor 1 and the number itself. Prime factorization is a method of finding factors of given numbers in terms of prime numbers.