### Hello Friends, In this post we will discuss various " Methods Used to Find HCF of Two or More Numbers "

Let's start the session !

Mainly there are two methods used to find out HCF or GCF of two or more numbers which are as follows :

**1. PRIME FACTORIZATION METHOD**

**Step 1 :**Express each number as a product of prime numbers

**Step 2 :**Multiply the least power of all common prime factors of the required number to get HCF

Let's see with some examples !

**Question 1 :**Find the HCF of 12, 15 and 24 by prime factorization method

**Step 1 :**

Prime factors of 12 are 2 and 3 thus 12 can be expressed as 2 x 2 x 3

Prime factors of 15 are 3 and 5 thus 15 can be expressed as 3 x 5

Prime factors of 24 are 2 and 3 thus 24 can be expressed as 2 x 2 x 2 x 3

**Step 2 :**

Now the common prime factors among 12, 15 and 24 is 3, thus HCF of 12, 15 and 24 is 3

**Question 2 :**Find the HCF of 30, 45 and 90 by prime factorization method

**Step 1 :**

Prime factors of 30 are 2, 3 and 5 thus 30 can be expressed as 2 x 3 x 5

Prime factors of 45 are 3 and 5 thus 45 can be expressed as 3 x 3 x 5

Prime factors of 90 are 2, 3 and 5 thus 90 can be expressed as 2 x 3 x 3 x 5

**Step 2 :**

Now the common prime factors among 30, 45 and 90 are 3 and 5, thus HCF of 30, 45 and 90 is 3 x 5 = 15

**Question 3 :**Find the HCF of 36, 48 and 72 by prime factorization method

**Step 1 :**

Prime factors of 36 are 2 and 3 thus 36 can be expressed as 2 x 2 x 3 x 3 = 2

^{2}x 3^{2}
Prime factors of 48 are 2 and 3 thus 48 can be expressed as 2 x 2 x 2 x 2 x 3 = 2

^{4}x 3
Prime factors of 72 are 2 and 3 thus 72 can be expressed as 2 x 2 x 2 x 3 x 3 = 2

^{3}x 3^{2}**Step 2 :**

Now the least power of all prime factors are 2

Still any doubts ! Just comment in comment section below, we will try to resolve it as soon as possible

Let's see with an examples !

Divide 45 by 30, Remainder = 15

Divide 30 by 15, Remainder = 0, thus HCF of 30 and 45 is 15

Now divide 90 by 15, Remainder = 0, thus HCF of 30, 45 and 90 is 15

^{2}and 3, thus HCF of 36, 48 and 72 are 2^{2}x 3 = 12Still any doubts ! Just comment in comment section below, we will try to resolve it as soon as possible

**2. DIVISION METHOD**

**Step 1 :**Divide greater number by smaller number.**Step 2 :**Divide smaller number by remainder you get in Step 1 continue the cycle till remainder = 0**Step 3 :**Divide the next number by divisor which leads to remainder = 0 in Step 2Let's see with an examples !

**Question 4 :**Find the HCF of 30, 45 and 90 by division method**Step 1 :**Divide 45 by 30, Remainder = 15

**Step 2 :**Divide 30 by 15, Remainder = 0, thus HCF of 30 and 45 is 15

**Step 3 :**Now divide 90 by 15, Remainder = 0, thus HCF of 30, 45 and 90 is 15

Still any doubts ! Just comment in comment section below, we will try to resolve it as soon as possible

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**o choose LOUD STUDY.**

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