FINDING FACTORS OF A NUMBER

Finding factors of a number : 

Factors are numbers we can multiply together to get a number.

A multiple is the product of a number and any whole number except zero.

To find the factors of a number, we can follow the below steps 

Step 1 :

Use multiplication or division facts to find factors. Start with 1 x the given number. Every counting number has at least two factor 1 and the number itself. So, 1 and 8 are factors of 8.

Step 2 :

Test other factor pairs. The only possible whole number factors of 8 are numbers from 1 to 8.

Step 3 :

Continue until the factors repeat

Note :

A factor always divides the product without a remainder.

Question 1 :

Find the factors of 45 

Solution :

Hence, factors of 45 are 1, 3, 5, 9, 15, 45. 

Question 2 :

Write the factors of 15

Solution :

15 = 1 x 15

15 = 5 x 3

Hence, factors of 15 are 1, 3,5 and 15.

Question 3 :

Write the factors of 18

Solution :

18 = 1 x 18

18 = 2 x 9

18 = 3 x 6

Hence, factors of 18 are 1, 2, 3, 6, 9 and 18.

How to find how many factors are in a number?

If the given number is small, it is easy to find number of factors. But for larger numbers, we can't just count one by one. This is a nice trick to find how many factors are in an integer.

To find the number of factors of an integer, we need to follow the steps given below.

Step 1 : 

Split the given number as prime factors using prime factorization method or tree method.

Step 2 : 

Take all exponents and add one to each of them.

Step 3 : 

Multiply the modified exponents together.

Let us see an example to understand the above method

Question 4 :

Find the number of factors of 48

Solution :

To get the number of factors of 48, first we have to find the factors.

48  =  1 ⋅ 48

48  =  2 ⋅ 24

48  =  3 ⋅ 16

48  =  4 ⋅ 12

48  =  6 ⋅ 8

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Number of factors of 48 = 10

We can get the same answer in the below method too.

Step 1 :

For that, first we have to split the given number 48 as prime factors using prime factorization method.

Step 2 :

48  =  2⁴ x 3¹

Take all exponents and add one to each of them. So, we get 2⁵ x 3²

Step 3 :

Multiplying the modified exponents, we get 5 x 2 = 10.

Hence the number of factors of 48 is 10.

Related Topics

After having gone through the stuff given above, we hope that the students would have understood how to find the factors of a number.

Apart from the stuff, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6