Question

Find the H.C.F of the following numbers by prime factorisation and continued division method.

18, 27, 36

Accepted Answer

We have to find the H.C.F of the numbers $18, 27, 36$ by both prime factorization and continued division method.

First, we shall use the prime factorization method:

Thus, we get,

Hence, the prime factors of $18$ are $2, 3 & 3$ and we write $18 = 2 \times 3 \times 3$ .

And,

Hence, the prime factors of $27$ are $3, 3 & 3$ and we write $27 = 3 \times 3 \times 3$ .

Also, we get,

Hence, the prime factors of $36$ are $2, 2, 3 & 3$ and we write $36 = 2 \times 2 \times 3 \times 3$ .

Now, we observe that in numbers $18, 27 & 36$ , the common factors are $3 & 3$ .

Therefore, the H.C.F of the numbers $18, 27 & 36$ is $= 3 \times 3 = 9$ .

Now, we shall use the continued division method to find the H.C.F of $18, 27 & 36 .$

In this method (invented by the famous Greek mathematician Euclid), we shall divide the larger number by the smaller and then divide the previous divisor by the remainder until the remainder is $0 .$ The last divisor is the H.C.F of the numbers.

Hence, we shall proceed as follows:

Step $- 1$ : First find the H.C.F of any two numbers. Let us find the H.C.F of $18$ and $27$ .

We got reminder as $0$ .

So, $9$ is the H.C.F of the numbers $18$ and $27$ .

Step $- 2$ : Now, we shall find the H.C.F of $9$ and $36$ using the continued division method again.

Again, we obtained reminder $0$ .

Thus, we get, the H.C.F of $9$ and $36$ is $9 .$

Hence, the H.C.F of the given three numbers $18, 27$ and $36$ is $9$ .

Therefore, from both the prime factorisation and continued division method, we obtain, the H.C.F of the numbers $18, 27$ and $36$ is $9$ .

Telangana Board Solutions for Chapter: Playing with Numbers, Exercise 12: Exercise 12

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Playing with Numbers, Exercise 12: Exercise 12

Questions from Telangana Board Solutions for Chapter: Playing with Numbers, Exercise 12: Exercise 12 with Hints & Solutions

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