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:

A factorof 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:Number1and thenumber itselfarealwaysfactorsof any number.

PRIME AND COMPOSITE NUMBERS.

A prime number has exactly 2 factors, the number itselfand 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 RULES

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);

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 tofind a H.C.F. of small numbers, like 6 and 9 (it is 3) or 8 and 4 (it is 4).

FINDING THE H.C.F. OF BIG NUMBERS

For larger numbers you can use the following method:

Find all prime factors of both numbers.

Write both numbers as a multiplication of prime numbers.

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 multipleof 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.

Thecommon multiplesof 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.)

TheLowest 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!!!!!!

NUMBERS, POSITIONS AND COLUMNSOPERATIONS INVOLVING NATURAL NUMBERSMULTIPLESFACTORSPRIME AND COMPOSITE NUMBERSLOWEST COMMON MULTIPLE (L C M )HIGHEST COMMON FACTORNUMBERS POSITIONS AND COLUMNSIn 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, orplace, of a digit in a number written in standard form determines the actualvaluethe digit represents. This table shows the place value for various positions:Place (underlined)Name of Position10001000 0001000 000 000Fingers Easy Multiplication trick Video

FACTORAfactorof a given number is every number thatdivides exactlyinto 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: Number1and thenumber itselfare always factors of any number.PRIME AND COMPOSITE NUMBERS.A

prime numberhas exactly2 factors, the numberitselfand1.In other words, the prime number can be divided only by 1 and by itself.

NOTE:0and1arenotprime numbers.Example: 5 is a prime number, because the only factors it has are 1 and 5.

The prime numbers less than 20 are

2,3,5,7,11,13,17,19composite numberhasat least one more factorthat the number itself or 1.In fact, all whole numbers that are not prime are composite

exceptfor1and0,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 RULESThe simple divisibility rules will help you to find factors of a number.

The number is divisible by:

- 7 sorry, no rule (you have to divide);

Do the following quizz about divisibility2if the last digit is 0, 2, 4, 6, or 8 (example: 12346);3if the sum of digits in the number are divisible by 3(example: 1236, because 1+2+3+6 = 12 = 3 x 4);

4if the last 2 digits are divisible by 4(example: 897544, because 44 = 4 x 11);

5if the last digit is 0 or 5(example: 178965 or 40980);

6if it is divisible by 2 and 3;8if the last 3 digits are divisible by 8(example: 124987080, because 080 = 8 x 10;

9if the sum of digits is divisible by 9(example: 234612, because 2+3+4+6+1+2 = 18 = 9 x 2);

10if the last digit is 0(example: 99990 );

100if the last 2 digits are 0(example 987600);

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

COMMON FACTORSWhen 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

tofind a H.C.F. of small numbers, like 6 and 9 (it is 3) or 8 and 4 (it is 4).FINDING THE H.C.F. OF BIG NUMBERSFor larger numbers you can use the following method:

Find all prime factors of both numbers.Write both numbers as a multiplication of prime numbers.Find which factors are repeating in both numbers and multiply them to get H.C.FExample:Find the Highest Common Factor (H.C.F.) of 240 and 924.

Solution:

Finding all prime factors of 240:240 =

2x2x 2 x 2 x3x 5Finding all prime factors of 924:924=2x2x3x7x11Multiply 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 amultipleof 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 multiplesof two numbers aremultiples 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.)The

Lowest Common Multiple (L.C.M)is thesmallest number that is a common multipleof 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