Math often requires answers to be Reduced or in Simplest Terms.
It is commonly used with Fractions and Ratios.

The opposite of reduction is to SCALE UP. This is used for Scale Drawings, Proportions and adding and subtracting fractions (Common Denominator)

DIVISIBILITY Rules are also used with Prime Numbers, Least Common Multiples (LCM) or Least Common Denominator (LCD) and Greatest Common Factor (GCF).

If you know the Rules of Divisibility, you can quickly solve problems and determine if an answer will have a remainder.
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You may remember that Numbers may be EVEN: (0, 2, 4, 6, 8) and ODD: (1, 3, 4, 7, 9)

If you know the Factors of a number, you can also reduce or simplify.

Division by:
(0) ZERO is undefined:  You can not divided (Reduce a number by Zero)
(1) ONE: 1 goes into every number, so it is not useful for finding factors
(2) TWO: 2 is an EVEN number and will go into every other Even Number.
                    If the number is ODD, then division by 2 will have a remainder of 1, or as a fraction: 1/2, or Decimal: .5

(3) THREE: Sum of the Digits is divisible by 3. Add up the digits in the number.  If the Sum of the digits is divisible by 3, then the number is divisible by 3.  If you cannot tell, Add up the digits again. Dividing by 3 will have a remainder of 1 or 2.  This is a fraction of 1/3 or 2/3  and as a decimal of .333 and .666.
   Example:  247: 1 + 4 + 7 = 12:    1 + 2 = 3             
                     682: 6 + 8 + 2= 16:  1 + 6 = 7.  The Remainder is '1'  

(4) FOUR: It muse be an EVEN number and the Last 2 Digits must be Divisible by 4.
                   The remainder will be a 1, 2, or 4:  1/4=.25,  2/4 = 1/2 = .5, 3/4 = .75

(5) FIVE: The number ends in 0 or 5. (Remainder will be a 1, 2, 3, or 4): 1/5 =.2, 2/5=.4, 3/5=.6 and 4/5=.8

(6) SIX: The number must be divisible by BOTH 2 and 3.

(7) SEVEN: No good quick rule for Divisibility by 7
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(8) EIGHT: If the last 3 digits of a number are divisible by '8', then the entire number is divisible.
                    The number must be even.

(9) Nine: Sum of the Digits is divisible by 9. Like the Rule for 3.
              Example:  1395 = 1+3+9+5 = 18;  1+8 =9.  Any number divisible by '9' is also divisible by '3'
                                

(10): TEN: ends in a ZERO The remainder will be 1-9 or as  a decimal, .1, .2, .3

Revised: April 18, 2024