1. Multiples and Factors

2. Multiples
Multiples are what you get when you multiply a number by another one.
12 is a multiple of 3. It is also a multiple of 4, of 2 and of 6.
12.5 is not a multiple of any of those numbers
The opposite of multiples is:

3. Factors
Factors of a number are those numbers that will divide into it exactly
The factors of 6 are 1, 2, 3 and 6
The factors of 12 are 1, 2, 3, 4, 6 and 12
All numbers have factors, even if they are just the number and one.
Numbers that can only be divided only by themselves and one are called Prime Numbers

4. Prime Numbers
Prime numbers are very important and used extensively in cryptography
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Prime factors of a number are the factors of a number that are prime

5. Prime Factors
Working out all the prime factors of a number is quite simple
Divide the number by the smallest prime number that will divide into it.
Divide the result by the smallest prime number
Keep doing that until you end up with 1

6. Prime Factors Work out the Prime Factors of 56 2 56
Divide by the smallest prime; 2 2 28 2 14
Divide by the smallest prime; 7 7 7 1
The prime factors, then, are

7. Lowest Common Multiple (LCM)
The Lowest Common Multiple is the smallest number into which each of two given numbers will divide exactly.

8. Find the lowest common multiple (LCM) of 24 and 56
Find the Prime Factors of each number: 2 24 12 6 3 1 2 56 28 14 7 1
A common multiple must include the highest power of each prime factor.
The LCM of 24 and 56 = 2  2  2  3  7 = 168

9. Find the highest common factor (HCF) of 120 and 252
The Highest Common Factor (HCF) is the largest number which will divide exactly into each of the given numbers.
Find the highest common factor (HCF) of 120 and 252 2
120 60 30 3 15 5 1 2
252
126 3 63 21 7 1
120 = 23  3  5
252 = 22  32  7
Common factors are 22  3 = 12