[Maths Class Notes] on Factors of 96 Pdf for Exam

How do you find factors of a number without using a calculator?

 

One way to do it is to break the number into factors. We know that all the factors of 12 are 1, 2, 3, 4, 6 and 12.

 

But what if the number has an odd number of digits? Then there are three cases:

 

If the number has one factor less than or equal to 10, then the first factor is a digit or a sequence of digits. The second factor is the sum of two digits and the third factor is the sum of three digits. The fourth factor is the sum of four digits etc.

 

Factorization in Math

In mathematics and logic, factorization is a process of dividing a single number by a number of other numbers to produce a product. It is a generalization of division and a special case of a polynomial.

 

If you see the following number:

 

Then the problem is what factors will you get? So the factors will be in the form of 1, 4, 9, 16, 25, 36, 49, etc. These factors can be called the prime factors.

 

The prime factors are numbers which do not have any number multiplied with it in a multiplication that will give the number which we require. For example:

 

Let’s see how the factors for the given number are formed.

4 x 5 = 20

 

2 x 5 = 10

 

Then we form the product of these and we get the given number. Now these are the prime factors. In fact, factors are the factors of one. If we multiply the factor with one, then we will get the same number.

 

Now let’s look at other numbers which do not have the given number as factors. For example:

 

9 x 4 = 36

 

4 x 3 = 12

 

Then the product of these is 36 and these numbers are not the factor of the given number. So we say these numbers are the prime factors of the given number.

 

How to Find Factors

There are various methods to find factors. These methods are discussed in detail below.

 

One method to find the factors is the factorization method. This is the most common method to find the factors. Let’s understand the method.

 

In the question If we look at the factors of the given number, it is obvious that 4 is a factor and 3 is a factor. So, here we just need to multiply the factors and see what we get.

 

4 x 3 = 12

 

Now, since 12 is a multiple of 4 and 3, they are not the factors of the given number. So, these are the factors of the given number.

 

In prime factorization, we calculate the number using prime factors. For example, the number given in the question is 5. Factors of the number are 2 and 5. So, we need to multiply these to get the number.

 

2 x 5 = 10

 

Now 10 is not the factor of the given number. So we conclude that these are the factors of the given number.

 

Prime Factorization is useful if the number is not a multiple of the number itself. It is not necessary that the factors of the given number must be prime. However, if they are prime, then we will have to multiply them to find the factors.

 

Number factoring has many benefits. First, number factoring can also be used to find square root, square root of a square number, cube root, etc. Second, it is easy to understand by children. Third, you don’t need to look for the number. It can easily be carried out by using a pocket calculator. Thus, it is very useful.

 

First factor: 3

Second factor: 16

Third factor: 8

Fourth factor: 24

Fifth factor: 16

Sixth factor: 8

Seventh factor: 96

 

• To determine the first factor, you can multiply the whole number (96) by the first digit (3). The factor is 3.

• To determine the second factor, you can multiply the whole number (96) by the second digit (16). The factor is 4.

• To determine the third factor, you can multiply the whole number (96) by the third digit (8). The factor is 3.

• To determine the fourth factor, you can multiply the whole number (96) by the fourth digit (24). The factor is 4.

• To determine the fifth factor, you can multiply the whole number (96) by the fifth digit (16). The factor is 5.

• To determine the sixth factor, you can multiply the whole number (96) by the sixth digit (8). The factor is 3.

• To determine the seventh factor, you can multiply the whole number (96) by the seventh digit (96). The factor is 6.

• Thus the number has a factor of 7, since the whole number is 96, and the 7th digit (96) is 7.

Factors are those, which on multiplication gives the number which we require. There are different methods to find the factors of the given number. We can find factors by factorization method, by division method, by divisibility method, and by the prime factorization method. The factors of a number 96 are those numbers which on multiplication with each other gives us the number 96. The factors of 96 can be positive numbers or negative numbers. Fractions and decimal numbers are not considered as factors. However,  negative numbers are considered as factors because on multiplying two negative numbers we get a positive number.

 

Factors of 96 By Division

 

Divisibility Method

In this method, we will find the factors by checking its divisibility. 

 

Step 1: The first step is to write the number for which we need to find the factors.

Step 2: For finding the factors of 96 we will check if 96 is divisible by 2 or not. 

Step 3: If it is divisible by 2 then we have to divide it. Here 96 is divisible by 2 because it divides 96 completely.

Step 4: Now we will check whether it is divisible by 3 here 96 is also divisible by 3 by the divisibility rule.

Step  5: Since 96 is divisible by 2 it is also divisible by 4.

Step 6: 96 has 6 in its units place so by the divisibility rule it is not divisible by 5 because the number is divisible by 5 only if it has 5 or 0 in the units place.

Step 7: 96 is also divisible by 6 by checking the divisibility.

Step 8: Now by the divisibility test, 96 is not divisible by 7 as we divisible a decimal number on dividing.

Step 9: The number 96 is also divisible by 8 because it divides it completely.

Step 10: 96 is not divisible by 9 because by dividing 96 by 9 we are getting a remainder.

Step 11: It is also not divisible by 10 as it does not contain 0 in the units place.

Example:

Positive Factors of 96 can be Given as

 

The positive factors of 96 

 

Similarly, we will have negative factors of 96. 

 

The Negative Factors of 96

 

Prime Factorization

The prime factors of a number are the prime numbers which on multiplication gives us the original number. This is the simplest way to find the factors.