Question

Use Euclid’s division algorithm to find HCF of 399 and 56

Answer 1

Hint: Here in this question, we have to find the HCF (Highest common factor of x and y). first list out the common factors of both numbers 399 and 56. Then take out the highest factor in the common factors of both numbers. That taken number will be a required HCF of a given two number 399 and 56.

Complete step-by-step answer:
The largest positive integer which divides two or more integers without any remainder is called Highest Common Factor (HCF) or Greatest Common Divisor or Greatest Common Factor (GCF). To find HCF, we have two important methods which are the Prime factorisation method and the division method.
Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers. HCF of two positive integers a and b is the largest positive integer d that divides both a and b.
Now consider the given two numbers and then on dividing by the numbers we get in the form
Here we have to divide both numbers by a common number, and it should divide both the numbers. Now we divide both the numbers by 7, and we write the quotient.
\[
  7\,\,\,\left| \!{\underline {\,
  {399,\,56} \,}} \right. \\
  \,\,\,\,\,\,\,57,\,8 \\
 \]
Furthermore we can’t divide the numbers 57 and 8 by the common number so we are leaving the numbers as it is.
Therefore the HCF of 399 and 56 is 7.
We can also solve this by using the another method
Now consider the two numbers 399 and 56
The number 399 is written as
\[399 = 3 \times 7 \times 19\]
The number 56 is written as
\[56 = 7 \times 2 \times 2 \times 2\]
Observing the factors of two numbers 399 and 56
399 having one 3 factor, one 7 factor and one 19 factor and
56 having one 7 factor and three 2 factors
In both 399 and 56 one 7 factor is common, then common factors of 399 and 56 are
Common factors of \[\left( {399,56} \right) = 7\]
The Highest common factor, HCF of \[\left( {399,56} \right) = 7\].
So, the correct answer is “Option B”.

Note: We must know about the multiplication, division and tables of multiplication to solve the question. We should divide by the number by the least number and hence it is the correct way to solve the problem. The LCM is abbreviated as Least common factor and the HCF is abbreviated as Highest common factor.