MathWithNaziaa : Factors and Multiples

Factors and Multiples

Factors and multiples are two different terminologies . Factors and multiples are two key concepts which have been studied together. Factors are the numbers which divide the given number exactly, whereas multiples are the numbers which are multiplied by other numbers to get a specific number.

Factors : By definition,  a factor is a number that divides another number without leaving any reminder.  factors for always less than or equal to the  given number. In simple words, if a number(dividend) Is exactly divisible by any number(divisor) then the divisor  is a factor of that dividend. If any natural number has only two factors i.e 1 and the number itself as its factors. Such numbers are called prime numbers. 1 is a factor of every number.

 For example :  2 is a factor of 8 (ie)  2 divides it exactly giving 4 as a quotient and remainder 0 .  Alternatively 4 is also a factor of 8 as it gives to as a quotient and 0 as a remainder.

 Therefore, factors of 8 are : 1,2,4,8 .

               

 Let's learn an easier way to find the factors:

 For example:  

1. Find the factor of 36,  letters use the multiplication  tables to find the factors of 36.

                           1 x 36 = 36 

                           2 x 18  = 36

                           3 x 12 = 36 

                          6 x 6    = 36 

      

              Therefore the factors of 36 are 1, 2, 3, 6, 12,18, 36.

2. Find the factors of 48

                    1x48 =48

                    2x24 = 48

                    3x16 = 48

                   4x12 = 48

                    6x 8   = 48

          

          Therefore the factors of of 48 are 1,2,3,4,6,8,12,16,24,48

Points to Remember:

• 1 and the number itself are the factors of every number.

•  the factors are always less than or equal to the  given number.

•  all prime numbers have only two factors which is1, itself,  for example  factors of 7 =1,7

                factors of 13=1,13

 Multiples:  By definition,  a multiple is a number that when divided A certain number of times by another number no remainder is left.  In simple terms multiples are nothing but multiplication tables. Multiples are always greater than or equal to the given number.

For example:  the multiples of 5 - 5,10,15,20,25,.........

                       the multiples of  8 - 8,16,24,32,40,......

 points to Remember:

• Multiples are nothing but multiplication tables.

• Multiples are always greater than or equal to the  given number.

 Difference between factors and multiples:

Factors	Multiples
Factors are the numbers which are exactly divisible by the given number.	Multiples are the numbers obtained by multiplying by the other number.
The factor of a number is finite	The multiples of the number  are infinite.
The operator used  is division.	The operator used  is multiplication.
Factors are always less than or equal to the given number.	Multiples are always greater than or equal to the given number.

Tricky riddles for factors and multiples.

1. Factors of 90 are added together to make another factor of 90. What are the two factors?

2. What am I?I am a multiple of 4.I am between 25 and 50.I'm also a multiple of 10.

3. Two square numbers are added together to make a multiple of 9.What could the two square numbers be?