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.
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.
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.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
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
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
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
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 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