# Properties: Factors and Multiples

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__PROPERTIES OF FACTORS MULTIPLES__

__FACTORS__

**Property 1:** **1 is a factor of every number and is the only number, which has exactly one factor.**

Example: 34 = 1 x 34

**Property 2:** **Every number is a factor of itself. **

Example: 18 = 18 x 1

**Property 3:** **Every factor of a number is an exact divisor of that number.**

**Factors of 6 are 1,2,3,6. Each factor divides 12.**

**Property 4:** **Every factor of a number is less than or equal to the number.**

**Property 5:** **Factors of a given number are finite.**

Example factors of 6 are 1,2,3 and 6 only.

**Property 6:** **Every number other than 1 has atleast 2 factors, 1 and number itself.**

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**Property 7:** **Number which has only 2 factors, 1 and number itself, is called a PRIME number.**

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**Property 8:** **Number which has more than 2 factors is called a COMPOSITE number.**

__MULTIPLES__

**Property 1:** **Every multiple of a number is greater than or equal to that number.**

Example: Multiple of 5 = 5,10,15,20,

**Property 2:**** Every number is a multiple of itself.**

First multiple of the number is number itself.

Example: 23*1=23

**Property 3:**** The number of multiples of a given number is infinite.**

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**Property 4:**** Every number is a factor as well as a multiple itself.**

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__FEW MORE PROPERTIES__

**Property 1:** **If a number is divisible by another number, then it is also divisible by each of the factors of that number.**

Example: 516 is divisible by 12, so 516 is also divisible by 1,2,3,4,6.

**Property 2:** **If A, B, C are three Natural numbers such that A is divisible B and B is divisible by C, then A is also divisible by C.**

Example: 27 is divisible by 9 and 9 is divisible by 3, so 27 is also divisible by 3.

**Property 3: ****If a number is a factor of each of the 2 given numbers, then it is also a factor of the sum of those 2 given numbers.**

Example: 25 and 35 both are divisible by 5,

Sum of the numbers =25+35=60

So, 60 is also divisible by 5.

**Property 4: ****If a number is a factor of each of the 2 given numbers, then it is also a factor of the difference of those 2 given numbers.**

Example: 25 and 35 both are divisible by 5,

Sum of the numbers =35-25=10

So, 10 is also divisible by 5.

**Property 4: ****The H.C.F. of the given number is never greater than any of the numbers.**

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**Property 5: ****The L.C.M. of the given number is never less than any of the numbers.**

**Property 6: ****The H.C.F. of any 2 prime or co-prime numbers is always 1.**

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**Property 7: ****The product of HCF and LCM of 2 given numbers is equal to the product of the 2 given numbers.**

HCF*LCM = product of the numbers.

**Property 8: ****The L.C.M. of any 2 prime or co-prime numbers is equal to the product of those numbers.**

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