**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 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.

- Generating equivalent numerical expressions
- Use repeated multiplication
- Division facts
- Exponents
- Using exponents
- Finding the value of a power
- Finding the value of each power
- Find the missing exponent
- Find the missing base
- Finding the factors of a number
- Finding the prime factorization of a number
- using ladder diagram for prime factorization
- Order of operations
- Exploring the order of operations
- Evaluating the numerical expression
- Using exponents with parentheses

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

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