EASY WAY TO FIND FACTORS OF A LARGE NUMBER

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.

Example 1 :

Find the number of factors of 48.

Solution :

Method 1 :

Decompose 48 into prime factors as shown below. 

48  =  2⁴ x 3¹

Modified exponents are (4 + 1) and (1 + 1). 

That is, 5 and 2. 

Multiplying the modified exponents.

5 x 2  =  10

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. 

Example 2 :

Find the number of factors of 30.

Solution :

Decompose 30 into prime factors as shown below. 

30  =  2¹ x 3¹ x 5¹

Modified exponents are (1 + 1), (1 + 1) and (1 + 1). 

That is, 2, 2 and 2. 

Multiplying the modified exponents.

2 x 2 x 2  =  8

Number of factors of 30 is 8.

Example 3 :

Find the number of factors of 42. 

Solution :

Decompose 42 into prime factors as shown below. 

42  =  2¹ x 3¹ x 7¹

Modified exponents are (1 + 1), (1 + 1) and (1 + 1). 

That is, 2, 2 and 2. 

Multiplying the modified exponents.

2 x 2 x 2  =  8

Number of factors of 42 is 8.

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