Factors And Multiples of HCF And LCM

Factors are numbers that can be multiplied by each other (two or three of them) or stand-alone to form the original number. On the other hand, multiples are the numbers that are evenly divisible by the original number and leave no remainder. In mathematics, these both are considered as inverse terms as they are opposite in nature.

Writing back its history, multiplication was invented four years ago by the Babylonians. Factors and multiples are an important part of division and multiplication.

FACTS ABOUT FACTORS AND MULTIPLES

What are exactly factors and multiples? we will now list some facts about both:

Factors:

·  Every number has at least one factor

·  The original number is always the factor of itself

·   1 is a factor of every number in mathematics

·  Other than 1, every number has at least two factors. One will be 1 and the other will be the number itself

·   The factor of any number will always be less or equal to the original number

Multiples:

·  Any number is always the multiple of itself as any number multiplied by 1 is equal to itself.

·  1 is a factor of every number and every number is a multiple of 1

· Every multiple of a number that we take will always be greater or equal to the original number

·  0 will always be the multiple of any number, but never a factor except itself (zero)

MAJOR DIFFERENCE BETWEEN FACTORS AND MULTIPLES

·  Factors are the divisors of the number whereas, multiples are numbers that are obtained by multiplying a number to some other number.

· Factors are limited numbers ranging from 1 to the number itself whereas, multiples are infinite in the calculation because you can keep on multiplying the number to any certain number to obtain a multiple

·  Factors are always equal to or less than the number whereas, multiples are always equal to or greater than the number

· We find factors by the process of division whereas, we find the multiples by the process of multiplication.

SOLVED EXAMPLES

Example 1:

Find the factors of 12.

Solution:

The factors of 12 will be 1, 2, 3, 4, 6, and 12

The number of factors is 6

Example 2:

Find the factors of 90.

Solution:

The factors of 90 will be 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

The number of factors is 12

Example 3:

Find the first 5 multiples of 15.

Solution:

The first 5 multiples of 15 are 15, 30, 45, 60, and 90.

Example 4:

Find the first 10 multiples of 20.

Solution:

The first 10 multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200.

Example 5:

Find the factors and first 5 multiples of 45.

Solution:

The factors of 45 are 1, 3, 5, 9, 15, and 45

The first 5 multiples of 45 are 45, 90, 135, 180, and 225.

Example 6:

Find the factors for 14 and 16 and find HCF.

Solution:

14 = 1, 2, 7, 14

16 = 1, 2, 4, 8, 16

Hence, HCF of 14 and 16 is 2.

APPLICATIONS OF FACTORS AND MULTIPLES

Factors and multiples can be used to divide anything into equal parts, for example, for the arrangement of things around you in rows and columns, for making calculations, to find divisors for a specific number, comparing any two quantities in number. In mathematics, it is used as a divisor to find which number can divide that number without leaving a remainder. For multiples, they can be used to obtain the numbers that the number itself can divide evenly.

CONCLUSION

Numbers are a part of our everyday life. We are always surrounded by it. This concept of factors and multiples are used in everyone’s life in many different ways for many different aspects. The concept of finding factors is mostly used when you are arranging anything in any way. For example, arranging your clothes in the wardrobe, arranging books on the shelf, setting up any permutation and combination, etc.