top of page
LEARN MORE
Rules of Factoring

Factoring rules assist in quickly discover the divisor to simplfy equations.

Step One: 
Discover the rule to determine if a number can be divided into it.

Rule 1: 
all numbers are divisible by

1

Rule 2: 
if divisible by 2, then last digit is 0, 2, 4, 6, 8
 

Rule 3:
if divisible by 3, then the sum of the digits is divisible by 3

Rule 4: 
if divisible by 4, then the last
two digits is divisible by 4

Rule 5: 
if divisible by 5, then the last digit is 0 or 5

Rule 6: 
if divisible by 6, then digits are
divisible 2 and 3

Rule 7: 
if divisible by 7, double last digit, subtract remaining digits

Rule 8: 
if divisible by 8 then the last 3 digits is divisble by 8

Rule 9: 
if divisible by 9, then the sum of the digits is divisible by 9

Rule 10: 
if divisible by 10, then the last digit is 0 

Step Two:
What numbers is divisible 18?
What numbers is divisible 24?

1:   Rule 1 =  18/1 = 18 OR 1 * 18 = 18
2:  Rule 2 = yes; 18 ends in 8:  18/2 = 9 OR  2 * 9  =  18
3:  Rule 3 = yes; 1 + 8 = 9, 9/3 = 3:  18/3 = 6 OR  2 * 9  =  18
4:  Rule 4  = no; 1 + 8 = 9, 9/4 = 2 remainder 2  
5:  Rule 5 = no; last digit is 8
6:  Rule 6 = yes; follows rule 2 & 3: 18/6 = 3 OR 6 * 3 = 18
7:  Rule 7 = no; 8 + 8 = 16, 16 -1  = 15 (not divible by 7)
8:  Rule 8 = no; 1 + 8 = 9, 9/8 = 1 remainder 1
9:  Rule 9 = yes; 1 + 8 = 9, 9/9 = 1: 18/9 = 2 OR 2 * 9 = 18
10:  Rule 10 = no; last digit is 8

1:  Rule 1 =  24/1 = 24 OR 1 * 24 = 24
2:  Rule 2 = yes; 24 ends in 4:  24/2 = 12 OR  12 * 9  =  24
3:  Rule 3 = yes; 2 + 4 = 6, 6/3 = 2:  24/3 = 6  OR  3 * 6  =  24
4:  Rule 4 = no; 2 + 4 = 6, 6/4 = 1 remainder 2  
5:  Rule 5 = no; last digit is 4
6:  Rule 6 = yes; follows rule 2 & 3: 24/6 = 4 OR 6 * 4 = 24
7:  Rule 7 = no; 4 + 4 = 8, 8 - 2  = 6 (not divible by 7)
8:  Rule 8 = no; 2 + 4  = 6, 6/8 = 6 remainder 2
9:  Rule 9 = no; 2 + 4 = 6, 6/9 = 0.6 (not divisible by 9)
10:  Rule 10 = no; last digit is 4

Step Three:
Choose common factor
Choose the greatest common factor (GCF)

18:  1, 2, 3, 6, 9, 18
24: 1, 2, 3, 6, 24

18:  1, 2, 3, 6
24: 1, 2, 3, 6

6

Step Four:
What are the factors?

6 * 3 = 18
6 * 4 = 24

3, 4

Step Five:
Solve the expression

18 + 24 = (6 * 3) + (6 * 4)                      = 6 (3  +  4 ) 

5

  35 : (35 / 5 = 7)
  45: (45 / 5 = 9)

(5 * 9)

(5 * 7) 

EXAMPLES

bottom of page