Question

Find the HCF of the following numbers by factor method...

1). 7, 18

2). 70, 14, 35​

Answer 1

Answer:

Step-by-step explanation:

Factorise the given number by using prime numbers

70 =7 * 5 * 2

14 = 7 * 2

35 = 7*5

Which number is common in all the three scenarios? Yup, it's 7

So, HCF is 7(When more than one factors are common then consider the highest number or their multiplication if the factors are common to all the numbers)

There are three methods of finding H.C.F. of two or more numbers.

1. Factorization Method

2. Prime Factorization Method

3. Division Method

1. H.C.F. by factorization method

Let us consider an example.

Find the H.C.F. of 36 and 45.

Factor of 36 are →

1, 2, 3, 4, 6, 9, 12, 18, 36

Factor of 45 are → 1, 3, 5, 9, 15, 45

1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6

1 × 45, 3 × 15, 5 × 9

2. H.C.F. by prime factorization method

Let us consider an example.

Find the H.C.F. of 24, 36 and 48.

First we find the prime factors of 24, 36 and 48.

Method of H.C.F.

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

The common prime factors = 2, 2, 3

H.C.F. = 2 × 2 × 3 = 12

3. H.C.F. by division method

Let us consider a few examples.

1. Find the H.C.F. of 12 and 18.

H.C.F. by Division Method

Step I: Treat the smallest number i.e., 12 as divisor and the bigger number i.e., 18 as dividend.

Step II: The remainder 6 becomes the divisor and the divisor 12 becomes the dividend.

Step III: Repeat this process till the remainder becomes zero. The last divisor is the H.C.F.

2. Find the H.C.F. of 16, 18 and 24.

Highest Common Factor by Division Method

Step I: First we consider the first two numbers and follow the same step 1, 2 and 3 of the above example.

Step II: The H.C.F. of the first two numbers which is 2 becomes the divisor and the third number 24 becomes the dividend. This process is repeated till the remainder becomes 0. H.C.F. is the last divisor