The following are rules to determine if a number
is divisible by another without actually doing division. The rational for each
is explained following each rule. (These rules are
helpful for reducing fractions and factoring.)
1.) If a whole number has 0 as its
last digit, it is divisible by 10 and by 5.
2.) If a whole number has a 5 as its
last digit, it is divisible by 5.
3.) If the digits in the whole number
add to a number divisible by 3 then that number is divisible by 3.
4.) If the last digit of the whole
number is even, then that number is divisible by 2.
Examples:
12 divisible by 2, rule
4, also 3 rule 3
39 divisible by 3, rule
3 (3 + 9 =12, 3 * 4 = 12)
275 divisible by 5, rule 2
225 divisible by 5, rule 2
and 3 rule 3 (2+2+5 = 9)
250 divisible by 10 and 5,
rule 1
Comments: In what follows number means
"whole number"
Multiplying any number by 10 adds
appends a 0 to it. Therefore any number with a trailing 0 must be
divisible by 10. (rule 1)
Multiplying an even number by 5
results and a 0 in the 1's place and multiplying an odd number by 5
results in a 5 in the 1's place. Therefore any number training with a
5 or 0 must be divisible by 5. (rule 1 and 2)
Multiplying any number by 2 results in
another even number and 2 is the smallest factor of all these even
numbers. So if the last digit in a number is even, it must be
divisible by 2. (rule 4)
Rule 3 requires some number theory,
accept that it works.
This is another FREE ALGEBRA PRINTABLE presented to you from the
Algebra section of
K12math.com