Properties: Factors and Multiples

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.

 

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

 

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.

 

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

 

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.

 

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.

 

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.