Divisibility Properties
We have learnt many methods of multiplication, division and other calculations. However, some shortcuts are very useful in competitive exams that have multiple choice questions. For this, the process of elimination is important. Just by looking at the given choices we must try to eliminate those that cannot be right and narrow down our options. Divisibility properties help us in such situations.
A divisibility test is a rule to determine whether one whole number is divisible by another. It is a quick way to find factors of large numbers.
Divisibility RuleExample
A number is divisible by 2 if the156 is divisible by 2 since the last
last digit is 0, 2, 4, 6 or 8digit is 6
(even number)143 is not divisible by 2 as the last digit is 3 (an odd number)
A number is divisible by 3 if the165 is divisible by 3 since the sum sum of the digits is divisible by 3of the digits is 12 (1+6+5=12), and 12 is divisible by 3
125 = 1+2+5 =8
Since 8 is not divisible by 3, 125 is not divisible by 3
A number is divisible by 4 if the 316 is divisible by 4 since 16 is di
number formed by the last two digitsvisible by 4.
is divisible by 4421 is not divisible by 4 as 21 is not divisible by 4
A number is divisible by 5 if the195 is divisible by 5 since the last
last digit is either 0 or 5digit is 5
443 is not divisible by 5 since the last digit is not 0 or 5
A number is divisible by 6 if it168 is divisible by 6 since it is diis divisible by both 2 and 3visible by 2 (ends in an even number) and by 3 (the sum of the digits is divisible by 3)
A number is divisible by 8 if the7120 is divisible by 8 since 120 is
number formed by the last three digitsdivisible by 8
is divisible by 8
A number is divisible by 9 if the549 is divisible by 9 since the sum sum of the digits is divisible by 9of the digits is 18 (5+4+9=18), and 18 is divisible by 9
A number is divisible by 10 if the1,470 is divisible by 10 since the last digit is 0last digit is 0
We also have a rule to check whether a number is divisible by 7:
A number is divisible by 7 if you672 (double of 2 is 4, 67-4 = 63, double the last digit and subtract itwhich is divisible by 7 so 672 is difrom the rest of the number and thevisible by 7)
answer is 0 or divisible by 7905 (double of 5 is 10, 90-10 = 80, which is not divisible by 7 so 905 is not divisible by 7
All about 12
Today’s date being 12/12, let us see what is special about the number 12.
12 is a composite number.
It is the smallest number with exactly six divisors, its divisors being 1, 2, 3, 4, 6 and 12.
It is the first composite number of the form p2q; a square-prime, and also the first member of the (p2) family in this form.
12 = 22 x 3.
The number 12 is often used as a sales unit in trade, and is referred to as a dozen.
12 dozen is known as a gross.
But do you know that there are 13 items in a baker’s dozen?
12 is a super factorial, being the product of the first three factorials.
1! x 2!x 3!
= 1 x (1x2) x (1x2x3)
=1 x 2 x 6
= 12
Most calendar systems have 12 months in a year.
There are 24 hours in a day, 12 hours being half a day.
12 is the largest known even number expressible as the sum of two primes (5 + 7).