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Tricks for Divisibility

Some basics tips and tricks that you can use for divisibility
All whole numbers are divisible by 1.
A number is divisible by 2 if it’s even.
A non-zero number is divisible by 5 if it ends in 0 or 5.
In order to check the divisibility of a number by a composite number, divide the composite divisor into prime factors, which are co-prime and then check for its divisibility with each. For example, to check the divisibility of a number with 12, break down 12 into 3 and 4.

Tricks for Divisibility
an – bn is always divisible by a-b
8555 is divisible by 8-5= 3

Remember it by:
a3b3 is divisible by a-b
a2b2 is also divisible by a-b
an – bn is divisible by a+b when n is even
710 – 510 is divisible by 7-5= 2
Remember it by:
a3 – b3 is not divisible by a+b
a2 – b2 is also divisible by a+b
a4 – b4 is also divisible by a+b

an + bis divisible by a+b when n is odd
711 + 511 is divisible by 7+5= 12
Remember it by:
a3 + b3 is divisible by a+b
a2 + b2is NOT divisible by a+b
a4 + b4 is NOT divisible by a+b

an + bn+cnis divisible by a+b+c when n is odd.
73 + 53 + 23= 343+125+8=476 divisible by 7+5+2=14

Questions you can solve by using above formula:
Example 1: 3223 + 1723is definitely divisible by….

a. 49
b. 15
c. 49 & 15
d. none of these.
As an + bn is divisible by a + b when n is odd
So 3223 + 1723 is divisible by 32 + 17 = 49.

Example 2: 3223 – 1723 is definitely divisible by….
a. 49
b. 15
c. 49 & 15
d. none of these.
As an – bn is always divisible by a-b.
So 3223 – 1723 is divisible by 32 – 17 = 15.

Example 3: 32232 – 17232 is definitely divisible by….
a. 49
b. 15
c. 49 & 15
d. none of these.

As an – bn is always divisible by a-b and an – bn is divisible by a + b when n is even
So 32232 – 17232 is divisible by both 32 – 17 = 15 and 32 + 17 = 49.

Example 4: 35 + 55+ 75is definitely divisible by….
a. 8
b. 7
c. 15
d. all of these.
As an + bn + cn is divisible by a + b + c when n is odd.
So 35 + 55 + 75 is divisible by 3 + 5 + 7 = 15

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