Factors and Multiples – An Extension

 

When you are asked to find the factors of 12, you are asked to find all those numbers that divide into 12 exactly, with no remainders:

Factors of 12 = 1, 2,  3, 4, 6, 12

Proof:  12 / 1 = 12,   12/2 = 6,    12/3 = 4,   12/4 = 3,   12/6 = 2,   12/12 = 1

 

This same concept holds true when the numbers/values being looked at are less concrete.

Factors of xy = 1, x, y, xy

Proof:  xy/1 = xy,   xy/x = y,    xy/y = x,    xy/xy = 1

The concept is the same, find all the values you can that will exactly divide your number… you don’t know what x is, but you know it is a component of xy (which means x times y) so you know it is a factor.

 

EXAMPLE:   The factors of 12xy are:  1, 2, 3, 4, 6, 12, 1x, 1y, 1xy, 2x, 2y, 2xy, 3x, 3y, 3xy, 4x, 4y, 4xy, 6x, 6y, 6xy, 12x, 12y, 12xy

 

FACTOR PAIRS are those two factors that, when one divides your number, it produces the other
EXAMPLE: The factor pairs of 12xy are: 

1  , 12xy               2  , 6xy                3  , 4xy                4  , 3xy               6  , 2xy               12  ,  xy

x  ,12y               2x , 6y                 3x  , 4y                4x , 3y                6x  ,  2y        12x  , y

 

 

 

Problems:

Find all the factors of these numbers

 

1) 2c                                                    2)  18m

 

 

 

3) 12c                                                  4) 25nw

 

 

 

 

5) avb                                                  6) cdef

 

 

Find the factor pairs for these numbers

7)  3c                                                   8) 6dw

 

 

 

9) 45k                                                  10) ax