Factors of 13—with Easy division and prime factorization

Factors of 13

Factors of 13 are numbers that divide the number 13 completely without leaving any residue. 

There can be positive and negative factors for 13, but they cannot be decimals or fractions. 

For example: 

The pair factors of 13 can be (1, 13) or (-1, -13). We can multiply the negative pair factors to get the original number. Therefore, multiplying -1 by -13 results in 13. 

In this article, we will learn how to use the division method and prime factorization method to calculate the factors of 13 and pair factors.

What are the Factors of 13?

Factors of 13 are the numbers multiplied in pairs to give the original number 13. Therefore, the factors of 13 are the numbers that divide 13 without leaving a remainder. Since 13 is a prime number, it has only two factors, one and the number itself. Therefore, it has two factors, 1 and 13.

What are the Factors of -13?

When we multiply two numbers and get -13 as a product, those numbers are the factors of -13. Here is the explanation:

-1 × 13 = -13

 1 × -13 = -13

We can get -13 by having (-1, 13) as a pair of factors. Similarly, we can also get -13 by having (1, -13)as a pair of factors.

Pair Factors of 13

When two numbers are multiplied, they give the product value of 13. The pair factor 13 can be both a positive and a negative factor. The number 13 has a single pair factor because it is a prime number. 

Accordingly, it has the following positive pair factor:

Similarly, the negative pair factor of 13 is given below:

Factors of 13 by Division Method

In order to find the factors of 13, one of the methods is to divide. We need to find the number that divides 13 exactly without leaving any remainder using this division method. Let’s first divide 13 by 1, and then divide the number by the consecutive integers.

13/1 = 13 (Remainder is 0 and the factor is 1)

13/13 = 1 (Remainder is 0 and the factor is 13)

When we divide 13 by numbers other than 1 and 13, we are left with a remainder. Therefore, factors 13 are 1 and 13.

More factors

Factors of 42= 1, 2, 3, 6, 7, 14, 21, and 42.

Factors of 48= 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Factors of 64=  1, 2, 4, 8, 16, 32, 64. 

Factors of 96= 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.

Prime Factorization of 13

Prime factorization is the process of expressing a number as the product of its prime factors. 

Here is the prime factorization of 13:

Step 1: 

Write down the pair factor of 13, let’s say (1, 13)

Step 2: 

The numbers 1 and 13 are both prime numbers, which cannot be further divided. To write down the factors, multiply 1 by 13.

As a result, 13 is equal to 1 × 13

Therefore, the prime factorization of 13 is 1 x 13 or 131.

Solved Examples

Example 1:

Find out the common factors of 13 and 26.

Solution:

Factors 13 are 1 and 13

The factors of 26 are 1, 2, 13 and 26

Thus, the common factors of 13 and 26 are 1 and 13.

Example 2:

Calculate the common factors of 13 and 17.

Solution:

Factors of 13 are 1, 13

Factors of 17 are 1, 17.

Due to both numbers being prime numbers, they have a factor of 1.

Therefore, the common factor of 13 and 17 is 1.

Example 3:

Calculate the common factors of 13 and 39.

Solution:

The factors 13 = 1 and 13

The factors of 39 = 1, 3, 13, and 39

Therefore, the common factors of 13 and 39 are 1 and 13.

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