EDEXCEL MATHS B: UNIT 2: Important Types of Numbers

EDEXCEL MATHS B: UNIT 2: Important Types of Numbers

PRIMES,MULTIPLES,FACTOR AND PRIME PRODUCT DECOMPOSTION, LCM AND HCF, SQUARE NUMBERS

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  • Created on: 13-11-12 16:18
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Important Types of Numbers
FACTOR ­ A factor of a number will divide exactly into the number.
Example ­ The factors of 12 are 1, 2, 3, 4, 6 and 12
PRIME NUMBER ­ A number with exactly two factors.
Example ­ 11 is a prime number as its only factors are 1 and 11.
The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
One is not a prime number as it only has one factor.
Two is the only even prime number
MULTIPLES ­ These are numbers with a common factor (alternatively they are numbers in
the appropriate `times table').
Example ­ The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24 ..........
PRIME FACTORS ­ These are factors of a number which are also prime numbers.
Example ­ The factors of 20 are 1, 2, 4, 5, 10 and 20
The prime factors of 20 are 2 and 5 (the prime numbers from the list of factors)
PRIME FACTOR DECOMPOSITION (or PRODUCT OF PRIMES)
Any nonprime number (except 1) can be written as the product of its prime factors.
We use a `factor tree' to help find the prime factors. Each number is written as a multiplication.
If one of the numbers is prime then that branch ends. It can help to circle the prime ends of the
branches.
Example ­ Express 120 as a product of its prime factors
120 120
2 60 3 40
2 30 4 10
2 15 2 2 2 5
3 5
120 = 2 x 2 x 2 x 3 x 5 = 23 x 3 x 5 120 = 2 x 2 x 2 x 3 x 5 = 23 x 3 x 5

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It does not matter which path you take, if your multiplications are correct, you will always get
the same answer.
If you want to look smart, write your answers using powers.
LOWEST COMMON MULTIPLE ­ The smallest value which is a multiple of both
numbers.
Example ­ Find the lowest common multiple of 2 and 5
Multiples of 2: 2 4 6 8 10 12 14 16 18 20 22 ......
Multiples of 5: 5 10 15 20 ......…read more

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Past Paper Questions
108
2 54
2 27 108 = 2 x 2 x 3 x 3 x 3
3 9 = 22 x 32
3 3
Factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
Largest of these which divides exactly into 108 is 36 so the HCF of 108 and 72 is 36
From `factor tree' we get: 24 = 2 x 2 x 2 x 3 = 23 x 3
Multiples of 24: 24,…read more

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