**Factors and Multiples**

**Factors**

Factors are the group of numbers for which given number is completely divisible, 1 and number itself are also including in that group.

**Let’s see some example:-**

Factor of 6 = 2 x 3 and 6 = 1 x 6 so in complete form we can write the factors of 6 are 1, 2, 3, 6

Factor of 32 = 1 x 32, 2 x 16, 4 x 8, so total factors of 32 are 1, 2, 4, 8, 16, 32

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**Highest common factor:-**

Highest common factor is the greatest factor which is common in all the factors of given numbers.

**Let see an example:**

Highest common factor of 18 and 42

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

Now we can see that there common factors are 1, 2, 3 and 6 (factors found in both numbers factor list ) but greatest factor is 6 So HCF of given numbers is 6.

**Multiples **

Multiples of a number is the set of number which are completely divisible by that number, or in other words we can say that multiple is the set of number where given number is multiplied with an integer.

**Let’s see some example:-**

Multiples of 3 are 3, 6 , 9, 12, 15, 18, 21,…..

Multiples of 7 are 7, 14, 21, 28, 35, 42,…..

Multiples of 14 are 14, 28, 42, 56,…….

**Lowest common multiple:**

It is the smallest common multiple in the multiples of the given numbers.

**Let’s see an example:-**

LCM of 4 and 6

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…….

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42……

Now we can see that there 12, 24, 36 … are the common multiples but smallest common multiple is 12 so LCM of given numbers is 12.