12 Divisibility Properties of Fibonacci Numbers You Should Know.

Welcome to MATH CLINIC!! We will be discussing about Life’s defining number…THE FIBONACCI NUMBERS. The Fibonacci numbers, named after the 13^th century mathematician, Leonardo of Pisa or Leonardo Fibonacci are the sequence of numbers;

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 . . .

These numbers are constructed such that the sum of the two previous term equals the next term

i.e 1 + 1 = 2,      1 + 2 = 3,    2 + 3 = 5 . . .

 

These numbers have variegated applications in nature, music etc. It is also a basis for the derivation of the Golden ratio which I call the building block of man (A discussion for some other time). If you quite familiar with the movie DA VINCI CODE, you definitely know Fibonacci numbers can be used to pass encrypted messages to loved ones.

Interestingly, these numbers like every beautiful concept have beautiful properties.

Let’s check them out!!

Property 1: Every third Fibonacci number is even.

Property 2: Every fifth Fibonacci number is divisible by 5.

Property 3: No odd Fibonacci number is divisible by 17 and 61.

Property 4: Every fourth Fibonacci number is divisible by 3.

Property 5: Every 6^th Fibonacci number is divisible by 4.

Property 6: Every 7^th Fibonacci number is divisible by 13.

Property 7: Every 8^th Fibonacci number is divisible by 7.

Property 8: Every 9^th Fibonacci number is divisible by 17.

Property 9: Every 10^th Fibonacci number is divisible by 11.

Property 10: Every 12^th Fibonacci number is divisible by 6,9, 12 and 16.

Property 11: Every 14^th Fibonacci number is divisible by 29.

Property 12: Every 15^th Fibonacci number is divisible by 10 and 61.

 

Hope you had a great time learning something new...

Smile Math Is Lovely and Entertaining (SMILE).