Exam Questions - Divisibility and multiple tests

Divisibility Tests

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
A number is divisible by 3 if the sum of its digits is divisible by 3.
Divisibility by 4 can be established if the number formed by the last two digits is divisible by 4.
A number is divisible by 5 if its last digit is 0 or 5.
For divisibility by 6, the number must be divisible by both 2 and 3.
A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
Divisibility by 9 is confirmed if the sum of the digits is divisible by 9.
A number is divisible by 10 if it ends in 0.

A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is divisible by 11.
To test divisibility by 12, a number must be divisible by both 3 and 4.

To determine multiples of a number, multiply the number by the set of integers. For instance, multiples of 2 are the even numbers.
The Least Common Multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers.
The LCM can be found by listing the prime factors of each number, then multiply each factor the greatest number of times it occurs in either number.

The Factors of a number are all the integers that can divide evenly into that number.
To find the factors of a number, begin by dividing it by 2, and continue with subsequent integers until reaching a number where division results in a fraction.
The Highest Common Factor (HCF) between two numbers is the biggest number that will divide both numbers.
To find the HCF, make a list of all prime factors for both numbers, then determine the shared factors. The HCF is the product of the shared factors.