NUMBERS POSITIONS AND COLUMNS
In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right.


Place Value

The position, or place, of a digit in a number written in standard form determines the actual value the digit represents. This table shows the place value for various positions:

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Place (underlined)
Name of Position
1 000
Ones (units) position
1 000
Tens
1 000
Hundreds
1 000
Thousands
1 000 000
Ten thousands
1 000 000
Hundred Thousands
1 000 000
Millions
1 000 000 000
Ten Millions
1 000 000 000
Hundred millions
1 000 000 000
Billions

Fingers Easy Multiplication trick Video



FACTOR

A factor of a given number is every number that divides exactly into that number.

Example

Write down all factors of 10.
10 = 2 x 5, so numbers 2 and 5 are factors of 10.

Also 10 = 10 x 1, so 10 and 1 are factors of 10.
The factors of 10 are 1, 2, 5, 10.
NOTE: Number 1 and the number itself are always factors of any number.

PRIME AND COMPOSITE NUMBERS.391490.jpg


A prime number has exactly 2 factors, the number itself and 1.

In other words, the prime number can be divided only by 1 and by itself.

NOTE:0 and 1 are not prime numbers.
Example: 5 is a prime number, because the only factors it has are 1 and 5.
The prime numbers less than 20 are 2,3,5,7,11,13,17,19

Acomposite numberhasat least one more factor that the number itself or 1.

In fact, all whole numbers that are not prime are composite exceptfor 1 and 0, which are not prime and not composite.
The composite numbers less than 20 are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18


DIVISIBILITY RULES404632_med.png


The simple divisibility rules will help you to find factors of a number.
The number is divisible by:
  • 2if the last digit is 0, 2, 4, 6, or 8 (example: 12346);
  • 3 if the sum of digits in the number are divisible by 3
    (example: 1236, because 1+2+3+6 = 12 = 3 x 4);
  • 4 if the last 2 digits are divisible by 4
    (example: 897544, because 44 = 4 x 11);
  • 5 if the last digit is 0 or 5
    (example: 178965 or 40980);
  • 6 if it is divisible by 2 and 3;
  • 7 sorry, no rule (you have to divide);
  • 8 if the last 3 digits are divisible by 8
    (example: 124987080, because 080 = 8 x 10;
  • 9 if the sum of digits is divisible by 9
    (example: 234612, because 2+3+4+6+1+2 = 18 = 9 x 2);
  • 10 if the last digit is 0
    (example: 99990 );
  • 100 if the last 2 digits are 0
    (example 987600);
Do the following quizz about divisibility

http://www.mathgames4children.com/Quizzes/Quizzes_by_topic/Counting%20&%20Number%20theory/Number%20theory/Divisibility/Divisibility/index.html
COMMON FACTORS

When two (or more) numbers have the same factor, that factor is called acommon factor.

Example


Find all the common factors of 12 and 18.
Factors of 12 are 1, 2, 3, 4, 6, 12.

Factors of 18 are 1, 2, 3, 6, 18.

The common factors of 12 and 18 are 1, 2, 3 and 6.


HIGHEST COMMON FACTOR (H.C.F).


The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers.

In other words the H.C.F is the largest of all the common factors.
The common factors or of 12 and 18 are 1, 2, 3 and 6.

The largest common factor is 6, so this is the H.C.F. of 12 and 18.
It is very easy to find a H.C.F. of small numbers, like 6 and 9 (it is 3) or 8 and 4 (it is 4).


HCF.jpg

FINDING THE H.C.F. OF BIG NUMBERS


For larger numbers you can use the following method:
  1. Find all prime factors of both numbers.
  2. Write both numbers as a multiplication of prime numbers.
  3. Find which factors are repeating in both numbers and multiply them to get H.C.F

Example:


Find the Highest Common Factor (H.C.F.) of 240 and 924.
Solution:
Finding all prime factors of 240:
240 = 2 x 2 x 2 x 2 x 3 x 5
Finding all prime factors of 924:
924=2x2x3x7x11





Multiply the factors which repeat in both numbers to get the H.C.F.

The Highest Common Factor is 2 x 2 x 3 = 12


MULTIPLES. COMMON MULTIPLES.


When you multiply a given whole number by any other whole number, the result is a multiple of that number.

For example, 5 is the first multiple of 5 (because 5 x 1 = 5),

10 is the second multiple of 5, and so on.

Example :

Write down the first 3 multiples of 8.

Solution: 8 x 1 = 8, 8 x 2 = 16, 8 x 3 = 24, so the first 3 multiples of 8 are 8,16,24.

The common multiples of two numbers are multiples of both numbers.
Example :

Find common multiples of 3 and 5.

Solution: Multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,...

Multiples of 5 are 5,10,15,20,25,30,35,...

Common multiples of 3 and 5 are 15, 30, ...

LOWEST COMMON MULTIPLE (L.C.M.)lcmlogo.gif


The Lowest Common Multiple (L.C.M)is the smallest number that is a common multiple of two or more numbers.
For example, the L.C.M of 3 and 5 is 15 .(see the example above).


The simple method of finding the L.C.M of smaller numbers is to write down the multiples of the larger numberuntil one of them is also a multiple of the smaller number.

Example :

Find the Lowest Common Multiple of 8 and 12.
Solution: Multiples of 12 are 12, 24...

24 is also a multiple of 8, so the L.C.M of 8 and 12 is 24.


And now try to learn this song about numbers,
Enjoy!!!!!!


The number rhumba