Exercise 1.5 Primes, Powers And Square Roots Worksheet - Heinemann Maths Zone
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11Prime numbers
We give special names to numbers depending on how many factors they have.
A prime number has exactly two factors: itself and 1.
A composite number has more than two factors.
1 is a special number—neither prime nor composite.
Prime factors and factor trees
A prime factor of a number is a factor that is also prime. Every composite
number can be expressed as a product of prime numbers.
A factor tree is a good way to find these prime factors.
worked example 10
Write 24 as a product of prime factors.
Steps
Solution
1. Break the number into a pair of factors
24
24
(not using 1), then break each
12
2
8
3
subsequent factor into a pair of factors.
Circle any prime factors as they
or
6
2
4
2
appear, and stop the branch at this
point. (Two possible trees are shown.)
3
2
2
2
24 = 2 × 2 × 2 × 3
2. Write the number as a product of the
circled factors.
e
eTutorial
e
Powers
eTutorial
2
Powers are a short way of writing repeated factors. 5
is an
index
example of a power. The small 2 is the index and tells us
2
5
how many factors of 5 there are. The 5 is called the base.
base
= 4 × 4
2
For example:
4
power
= 5 × 5 × 5
3
5
= 7 × 7 × 7 × 7
4
7
= 9 × 9 × 9 × 9 × 9
5
9
●
17
1
w h o l e
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