Factors, Multiples, Prime Factorization

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 00, a dividend is "divisible" by a divisor.

The divisors that divide, with remainder 00, are called **factors** of the dividend.

eg: Factors of 66 are 11, 22, 33, 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,⋯

"6, 12, 18, 24, 30, ⋯ "

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,⋯".

The multiples of 34 are "34,68,102,136,⋯".

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.

4×6

2×4×3

3×8

and more like 2×12

The following is a product of prime numbers

"2×2×2×3". 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 2×2×2×3×11".

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__