Factors and Multiples
Factors
A factor of a number will divide that number exactly, without any remainder.
Example : 2 is a factor of 16 because 2 goes into 16 exactly 8 times, with no remainder.
But note that 16 also has other factors apart from 2. These other factors are
 4 : which goes into 16 exactly 4 times
 8 : which goes into 16 exactly 2 times
 as well as 16 itself : 16 divided by 16 equals 1
 and also 1 : 16 divided by 1 equals 16
So the number 16 has a total of 5 factors.
Example : 24 has the following factors
1,2,3,4,6,8,12,24
Example : 3 is a factor of 9 because 3 divides into 9 exactly, without any remainder.
Example : 3 is also a factor of
27, 18, 30, 15,....and many more
Which of the following are factors of 72 ?

4 is a factor of which of these numbers ?

Highest Common Factor
The Highest Common Factor (HCF) of two numbers is the highest number that is a factor of both numbers
Example : The numbers 36 and 24 have a common factor of 4. But this not the Highest Common Factor, because 6 is also a common factor. The number 6 itself is still not the required HCF  the HCF is actually 12.
Finding Factors of Large Numbers
Some rules
First the easier ones
 2 is a factor of all even numbers
 10 is a factor of all numbers ending in 0
 5 is a factor of all numbers ending in a 0 or 5
 3 is a factor
of a number if it is also a factor of the sum of the individual digits in the number, e.g
 65421 (digits add up to 18)
 24 (digits add up to 6)
 321 (digits add up to 6)
 9 is a factor of a number if it is also a factor of the sum of the individual
digits in the number, e.g.
 76437 (digits add up to 27)
 27 (digits add up to 9)
 981 (digits add up to 18)
 11 is a factor of a three figure number if the middle digit is the sum of the two outside digits, e.g. 792
Multiples
Multiples of a number are obtained just by multiplying that number by a whole number.
Example The multiples of 6 are
6, 12 , 18, 24, 30, etc
Note that 6 is a multiple of 6 because it is equal to 6 multiplied by one.
Which of the following are multiples of 7 ?

Lowest Common Multiple
The Lowest Common Multiple (LCM) of two numbers is a multiple of both numbers and lower than all other numbers that are also multiples of both the numbers.
Example The Lowest Common Multiple of 6 and 4 is 12.
12 is lower than other common multiples like 24, 36, 48, and there is no common multiple of 6 and 4 which is lower than 12.