About "Easy way to find factors of a large number"

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.

How to find how many factors are in 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 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.

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