FACTORS AND MULTIPLES

FACTORS, MULTIPLES AND DIVISORS

When two or more numbers are multiplied together the result is called the product that is to say given two natural  numbers  A and B  their product is  C or C=AXB. 

for example 

(i)The product of 4 and 3 is 12 i.e. 4x3=12.

(ii)The product of 2, 5 and 6 is  60 i.e. 2 x 5 x 6 = 60.
A and B are called factors of the product C, and C ,the product, is called the multiple of each of the factors A or B
So, for  4x3=12,  4 is a factor of 12 and 12 is a multiple of 4.Similarly 3 is a factor of 12 and 12 is a multiple of 3

Thus a natural number that divides another number exactly is called a factor (or a divisor in the case of division) of that number, and the given number is called a multiple of that number.
Hence, A is a factor of C because on dividing  C by A, the remainder is zero

for example since
(i)4x3=12 and 12x1=12, 1, 3, 4 and 12 are all factors (or divisors) of 12 and 12 is a multiple of each of the numbers 1, 3, 4, and 12.
(ii)2x4=8 2x2x4=8, and 1x8=8, 1, 2, 4, and 8 are all factors of 8 and 8 is a multiple of each of the number 1, 2, 4, and 8.

Similary
18 has factors f18={1, 2, 3, 6, 9, 18}.

42 has factors f42={1, 2, 3, 6, 7, 14, 21, 42}.

2 has multiples M2={2, 4, 6, 8, 10,...., 2n} where n is an integral number. 

6 has multiples M6={6, 12, 18, 24,...., 6n} where n is an integral number. 

from the above results we can conclude that :

(i)one is a factor of every number.

(ii)The only factor of one is one itself.

(iii)Every natural number is a factor of itself.

(iv)Every number has at least two factors, namely 1 and itself.

(v)Every factor of a number is less than or equal to that number.

(vi)Every number has a finite number of factors.

(vii)Every number is a multiple of itself.

(viii)Every multiple of a number is greater than or equal to the  and  number 
itself.

(ix)Every number has an infinite number of its multiples.