**Highest common factor :**

We know that different numbers have common divisors. Among the common divisors the greatest divisor is the G.C.D.

There are two methods to find G.C.D of the given numbers.

(i) Common divisor method

(ii) Factorization method

(iii) Using ladder diagram method

Now let us see the above methods one by one.

We have to follow the steps given below, when we use common multiple method to find the H.C.F of two or more numbers.

**Step 1 :**

Find the divisors of the given numbers.

**Step 2 :**

Circle and write the common divisors

**Step 3 :**

Among the common divisors the greatest divisor is the G.C.D.

**Example 1 :**

Find the H.C.F of 16 and 24 using common divisor method.

**Solution : **

Divisors of 16 = 1, 2, 4, 8, 16

Divisors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Common divisors = 2, 4, 8

H.C.F = 8

Hence the H.C.F of 16 and 24 is 8.

We have to follow the steps given below, when we use factorization method to find the H.C.F of two or more numbers.

**Step 1 :**

Find the prime factors of the given numbers.

**Step 2 :**

Circle the common factors.

**Step 3 :**

Product of common factors is the G.C.D of the given numbers.

**Example 2 :**

Find the H.C.F of 16 and 24 using factorization method.

**Solution : **

Factors of 16 = 2 x 2 x 2 x 2

Factors of 24 = 2 x 2 x 3 x 2

Common factors = 2 x 2 x 2

H.C.F = 8

We use the steps given below to do prime factorization using ladder diagram.

**Step 1 : **

Put the given numbers inside the "L" shape

**Step 2 :**

We have to split the given number by prime numbers only. That is, always we have to put prime numbers out side the "L" shape.

Given below will be helpful to find the prime number which exactly divides the given number.

- A number which ends with 0, 2, 4, 6 and 8 is divisible by the smallest prime number 2.
- A number which ends with 0 or 5 is divisible by 5
- If the sum of digits of the given number is a multiple of 3, then the given number is divisible by 3.

**Step 4 :**

Repeat this process until get prime numbers inside the ladder.

**Step 5 :**

The product of numbers out side the ladder will be the H.C.F

**Example 3 :**

Find the L.C.M of 16 and 24 using ladder diagram

**Solution : **

H.C.F = 2 x 2 x 2

= 8

After having gone through the stuff given above, we hope that the students would have understood "Highest common factor".

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