**Easy way to find factors of a large 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.

**Factors :**

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

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 1 :**

Find the number of factors of 48

**Solution :**

**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.

**Method 2 :**

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

**Question 2 :**

Find the number of factors of 30

**Solution :**

**Step 1 :**

For that, first we have to split the given number 30 as prime factors using prime factorization method.

**Step 2 :**

30 = 2¹ x 3¹ x 5¹

Take all exponents and add one to each of them. So, we get 2 x 2 x 2.

**Step 3 :**

Multiplying the modified exponents, we get 8.

Hence, the number of factors of 30 is 8.

**Question 3 :**

Find the number of factors of 42

**Solution :**

**Step 1 :**

For that, first we have to split the given number 42 as prime factors using prime factorization method.

**Step 2 :**

42 = 2¹ x 3¹ x 7¹

Take all exponents and add one to each of them. So, we get 2 x 2 x 2.

**Step 3 :**

Multiplying the modified exponents, we get 8.

Hence, the number of factors of 42 is 8.

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

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