**Factors and Multiples :**

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.

**Question 4 :**

List the first 5 multiple of 8

**Solution :**

To get the first 5 multiple of 8, we need to multiply 8 by 1, 2, 3, 4 and 5 respectively.

1 x 8 = 8

2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

5 x 8 = 40

Hence, first 5 multiple of 8 are 8, 16, 24, 32 and 40.

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 5 :**

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 x 48

48 = 2 x 24

48 = 3 x 16

48 = 4 x 12

48 = 6 x 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 2**⁵** x 3²

**Step 3 :**

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

Hence, the number of factors of 48 is 10.

- Greatest common factors
- Least common multiple
- Prime factorization method
- Order of operation
- Multiplication facts
- Division facts

After having gone through the stuff given above, we hope that the students would have understood "Factors and multiples"..

Apart from the stuff given above, if you want to know more about "Factors and multiples", please click here

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

Widget is loading comments...

You can also visit our 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**