Divisibility in Whole Numbers : Factors, Multiples, Prime Factorization

maths > wholedivisors

Factors, Multiples, Prime Factorization

what you'll learn...

overview

This page provides a brief overview of factors of a number. multiplies of a number. prime factorization of numbers

Factors

When the remainder is $0$ $0$ , a dividend is "divisible" by a divisor.

The divisors that divide, with remainder $0$ $0$ , are called factors of the dividend.

eg: Factors of $6$ $6$ are $1$ $1$ , $2$ $2$ , $3$ $3$ , and $6$ . Because the remainder is $0$ for $6-:1$ , $6-:2$ , $6-:3$ and $6-:6$

eg: Factors of $20$ are $1$ , $2$ , $4$ , $5$ , $10$ , and $20$

eg: Factors of $13$ are $1$ and $13$

The word "factor" means "a part or component of something bigger".

Factors of a number : The divisor that divides with remainder $0$ , is a factor of the dividend.

the dividend, divisor are non-zero whole numbers.

The factors of $26$ are " $1, 2, 13, 26$ ".

The factors of $28$ ? are " $1,2,4,7,14,28$ ".

Multiples

Consider the number $6$ . The following shows result of multiplying $6$ by the sequence of numbers $1,2,3,4,5,cdots$
" $6$ , $12$ , $18$ , $24$ , $30$ , $cdots$ "

A dividend that has another number as factor is called multiple of the factor.

eg: $24$ is a multiple of $3$ , as $24-:3 = 8$ with remainder $0$

eg: $24$ is also a multiple of $2$

eg: $24$ is also a multiple of $6$

eg: $24$ is also a multiple of $24$

The word "multiple" means "having several parts of something".

Multiples of a number : The dividend that is divided by a factor with remainder $0$ , is a multiple of the factor.

The multiples of $6$ are " $6,12,18,cdots$ ".

The multiples of $34$ are " $34,68,102,136, cdots$ ".

Prime Factorization

The factors of $24$ are " $1,2,3,4,6,8,12,24$ "

Consider the number $24$ . Factors of $24$ are $1$ , $2$ , $3$ , $4$ , $6$ , $8$ , $12$ , and $24$ . The following ways, the number is expressed as a product of some of the factors.
$4xx6$
$2xx4xx3$
$3xx8$
and more like $2xx12$

The following is a product of prime numbers
" $2xx2xx2xx3$ ". The number $24$ is represented as product of prime factors. This is called prime factorization.

Prime Factorization : A number represented as product of prime numbers.

What is the prime factorization of $264$ ?
The answer is "product of $2xx2xx2xx3xx11$ ".
A procedure is illustrated in the figure.

What is the prime factorization of $17$ ?
Since $17$ is a prime number, the answer is " $17$ ".

summary

Factors of a number : The divisor that divides with remainder $0$ , is a factor of the dividend.

the dividend, divisor are non-zero whole numbers.

Multiples of a number : The dividend that is divided by a factor with remainder $0$ , is a multiple of the factor.

Prime Factorization : A number represented as product of prime numbers.

Outline

The outline of material to learn "Divisibility in Whole Numbers" is as follows.

Note: click here for detailed outline of Whole divisors

→ Classification as odd, even, prime, and composite

→ Factors, Multiples, Prime factorization

→ Highest Common Factor

→ Lowest Common Multiple

→ Introduction to divisibility tests

→ Simple Divisibility Tests

→ Simplification of Divisibility Tests

→ Simplification in Digits for Divisibility Tests