Question

The H.C.F of 252,324 and 594 is.
A) 36
B) 18
C) 12
D) 6

Answer 1

Hint: First we must find the factors of each of the numbers in the question separately. Later we must consider the common factors in all the numbers. The Product will give H.C.F.

Complete step-by-step answer:
(Step 1) We will use the method of prime factorization to solve where we will write the number as a product of its prime factors.
\[
   \Rightarrow 252 = 2 \times 2 \times {3^2} \times 7 \\
   \Rightarrow 324 = 2 \times 2 \times {3^2} \times {3^2} \\
   \Rightarrow 594 = 2 \times {3^2} \times 3 \times 11 \\
 \]
\[
   \Rightarrow 252 = 2 \times {3^2} \times 2 \times 7 \\
   \Rightarrow 324 = 2 \times {3^2} \times 2 \times {3^2} \\
   \Rightarrow 594 = 2 \times {3^2} \times 3 \times 11 \\
 \]
(Step 2) Now we will list all the factors which are common to all the numbers. Hence we will see from step 1 that the following common factors which are represented with red and factors that are not common in all three numbers can be represented in black color.
(Step 3) On finding the common factors from step 2 we will just multiply the numbers to get the desired H.C.F.
$\therefore $ H.C. F$ = 9 \times 2 = 18$

Final answer: The H.C.F of the three numbers is 18.

Note: The number which is greatest and will divide each of the two or more than two numbers is called HCF (or Highest Common Factor). Sometimes it is also called G.C.D (or Greatest Common Divisor) Important Point: There is one more thing i.e. LCM which is very frequently used with H.C.F. But remember both are different because in L.C.M we will need to find the least common multiple of given two or more numbers.
We can also find H.C.F by one more method which is a Division Method. This is nothing but simple division. We will simply write all the numbers in a line and divide it by prime number to get the quotient. We will repeat this process until no coprime is left. The Prime numbers by which we have divided our number will give us the required H.C.F.