Уроки математики и физики (RU + UA)

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понедельник, 14 ноября 2016 г.

Lesson 10. Factors and prime numbers

A factors is a numbers which divides exactly into another numbers (there will be no remainder)
If 2 divides into a number exactly, that number is an even number (2, 4, 6, 8).
If 2 does not divide into a number exactly, that number is an odd number (1, 3, 5, 7).
A prime number can only be divide by to different numbers (these are the numbers 1 and itself). The first four prime numbers are 2, 3, 5, 7.

EXAMPLE:

All the factors of 10 are 

1, 2, 5, 10.

Prime factors

Factors of a numbers which are also prime numbers are called prime factors. We can find these prime factors by using a 'factor tree' or by dividing by prime numbers again and again.

EXAMPLE:

Find the prime factors of 36.

METHOD 1:

Factor tree
Split into 4 and 9 because 4 × 9 = 36  
Split 4 into 2 × 2
Split 9 into 3 × 3
Stop splitting when all numbers are prime numbers
We can say 36 = 2 × 2 × 3 × 3

METHOD 2:

Dividing by prime numbers

Dividing by any prime number
Stop when you get 1
These are prime factors.
We can say 36 = 2 × 2 × 3 × 3

The product of prime factors

When we write 36 = 2 × 2 × 3 × 3, the prime factors 2,  2,  3 and 3 are multiplied together. This is called a product.
2 × 2 × 3 × 3 is the product of its prime factors.

Index form

 2 × 2 = 22    3 × 3 = 32
So 36 = 2 × 2 × 3 × 3 

 can be written as 22 × 32
The answer written like this using power is said to be in index form.

Tasks to the lesson 10
Other lessons:
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