Download Introducing prime factor trees Introducing prime

Christian Goldbach
Born: 18 March 1690 in Königsberg, Prussia
(now Kaliningrad, Russia)
Died: 20 Nov 1764 in Moscow, Russia
Introducing
prime factor
trees
The mathematician Goldbach said that
all even numbers above 2 can be
written as the sum of two primes:
e.g. 12 = 5 + 7
48 = 5 + 43
48 = 7 + 41
48Answers
= 11 + 37
48 = 17 + 31
48 = 19 + 29
List the five distinct ways in
which 48 can be expressed as
the sum of two primes.
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© www.teachitmaths.co.uk 2011
We use prime factor trees to help us:
1. Find two numbers that multiply to
give your original number. One of the
numbers must be prime.
Primes are the building blocks
for all natural numbers:
15
3. Repeat until all branches of
the tree end with circled
prime numbers.
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45
x
x
14
5
3
7
3
x
45 = 3 x 345x =5 = 32 x 5
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x
5
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Try this one:
It doesn't matter what order you find
the primes in:
9
45
2. Circle the prime number.
9=3x3
38 = 2 x 19
45 = 3 x 3 x 5
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2
Breaking a number into the product of its primes is called
prime factor decomposition.
Each integer can also be written as the product of
primes. This was discovered by the Greek
mathematician Euclid.
e.g.
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x
3
3
4
56
28
x
x
2
2
2
56 = 2 x 2 x562 =x 7 = 23 x 7
5
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1
Express each of the following as the product of primes:
50
30
105
52
63
81
Primes less than 100:
2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79,
83, 89, 97.
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