Factors of a Number

Factors are defined as numbers or algebraic expressions that divides a given number exactly. Here, a list of factors of numbers is given which will help to understand how to find the factors of a number and know the factors of some common digits. Before going to the explanations, it is important to know what does factor mean in math which has been explained below.

What is Factoring of a Number?

The factors of a number are defined as the number which can be multiplied to get the original number. By multiplying two factors a product is obtained. It should be noted that factors of any number can be either positive or negative. For example, in the case of 6, the factors can be 2 and 3 as 2 × 3 gives 6. Here, 2 and 3 are factors while 6 is the product. The other factors of 6 are 1 and 6, -2 and -3, etc.

How to Find Factors of a Number?

Knowing how to calculate factors of a number is extremely crucial in maths. The steps to find the factors of a number are given below in a very easy to understand way. An example is taken to make the explanation easier.

  • Step 1: Choose a number (say, 16)
  • Step 2: Write the common factors of 16 which will include (16 × 1), (-16 × -1), (8 × 2), (-8 × -2), (4 × 4), and (-4 × -4).
  • Step 3: Further factor the factors until a prime number is reached. In this case, 8 can be factored further.
  • Step 4: Write down all the factors again. The (8 × 2) will now become (4 × 2 × 2).
  • Step 5: Write all the unique number that is obtained.

So, the factors of 16 will be 1, 2, 4, 8, 16, – 1, – 2, – 4, – 8, and – 16. Here, the positive factors of 16 are only 1, 2, 4, 8, and 16.

Another Example:

Consider the number as 80.

80 = 10 × 4

= (5 × 2) × 8

=(5 × 2) × (4 × 2)

= (5 × 2) × (2 × 2 × 2)

Now, the factors of 80 will all the combination from 5 × 2 × 2 × 2 × 2 and 1 itself (as 1 × 80 = 80). So, the positive factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. It should be noted that there will also be negative factors whose count have to be even.

How to Calculate Factors of Large Numbers?

To calculate the factors of large numbers, divide the numbers with the least prime number i.e. 2. If the number is not divisible by 2, move to the next prime numbers i.e. 3 and so on until 1 is reached. Below is an example to find the factors of a large number.

Example: 1420

Steps Prime Factors Product
Step 1: Divide by 2 2 710
Step 2: Again Divide by 2 2 355
Step 3: Divide by 5 71

In step 3, a prime number is obtained as a product and so, the process is stopped. The factors will be all the multiples of 1, 2, 2, 5, 71, 355, 710. Now, the positive factors of 1420 will be 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, and 1420.

In the same case, if only prime factors are considered, it is called the prime factorization of that number. In this way, it is easy to factor a number and know its factors and prime factors.

Factors of Numbers

Below is a list of common numbers with their factors and prime factors. Each of these links will include the process of factoring of any number along with all the factors including the prime factors of that number.

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