Transcript Factors

Multiples and Factors
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:
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
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
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
Prime Factors
Work out the Prime Factors of 56
2
56
2
28
2
14
7
7
Divide by the smallest prime; 2
Divide by the smallest prime; 7
1
The prime factors, then, are
2 2 2 7
Lowest Common Multiple (LCM)
• The Lowest Common Multiple is the
smallest number into which each of two
given numbers will divide exactly.
Find the lowest common multiple
(LCM) of 24 and 56
Find the Prime Factors of each number:
2
24
2
56
2
12
2
28
2
6
2
14
3
3
7
7
1
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
Highest Common Factor
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
2
252
2
60
2
126
2
30
3
63
3
15
3
21
5
5
7
7
1
120 = 23  3  5
1
252 = 22  32  7
Common factors are 22  3 = 12