Question

What is the divisibility rule of 20?

Answer 1

Hint: We first describe the process of finding the prime factorisation of 20. Using the division, we find the multiplication form to find the divisibility rule of 20.

Complete step by step solution:
The process of finding the prime factorisation of a number is to find the smallest prime possible which divides the number. We complete the division then look for the same process again. We continue this process until we get 1 as the remaining quotient.
Therefore, if we need the prime factorisation of $ a $ and we find $ x $ to be the least prime that divides $ a $ , then we take $ \dfrac{a}{x} $ for the next step and find its least prime factor to continue the process.
At the end we write the prime in multiplied form to find the prime factorisation.
For our given 20, we find the prime factorisation using long division.
\[\begin{align}
  & 2\left| \!{\underline {\,
  20 \,}} \right. \\
 & 2\left| \!{\underline {\,
  10 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
Therefore, the prime factorisation of 20 is $ 20=2\times 2\times 5=4\times 5=2\times 10 $ .
The divisibility rules for 20 will be that the last two digits of the given number has to be divisible by 20 which means numbers having 00, 20, 40, 60, 80 at the end will be divisible by 20.

Note: We can also say that if the number is divisible by both 4 and 5 then the number is divisible by 20. 20 can be expressed as $ 20=4\times 5 $ of two prime numbers.