# Modulus Pattern for Divisibility

###### This wiki is incomplete.

There are a lot of divisibility rules floating around us. We knew exactly when a number is divisible by a certain divisor:

- A number is divisible by 2 if and only if it ends in 0,2,4,6, and 8.
- A number is divisible by 3 if and only if the digits of the number add up to a multiple of 3.
- A number is divisible by 4 if and only if the last two digits are divisible by 4.
- A number is divisible by 5 if and only if its last digit is either 5 or 0.

Also, we learned the other divisibility rules in large numbers through combining divisibility rules:

- A number is divisible by 14 if and only if it is both divisible by 7 and 2.
- A number is divisible by 100 if and only if the last two digits are both zeroes (both divisible by 25 and 4).
- A number is divisible by 143 if and only if it is both divisible by 11 and 13.
- A number is divisible by 42 if and only if it is both divisible by 6 and 7.

## Introduction

## Example Question 1

This is the answer to the question, with a detailed solution. If math is needed, it can be done inline: $x^2 = 144$, or it can be in a centered display:

$\frac{x^2}{x+3} = 4y$

And our final answer is 10. $_\square$

**Cite as:**Modulus Pattern for Divisibility.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/modulus-pattern-for-divisibility/