Factors Of 26 – With Division and Prime Factorization

Factors of 26

Factors Of 26

The factors of 26 are the numbers multiplied together to produce the original number. Positive and negative factors are both possible for 26. 

Pair factors can take two forms, for instance (1, 26) and (-1, -26). By multiplying -1 and -26, we get the original number 26. There are both positive and negative factors that can be found in 26. However, it cannot be expressed in decimals or fractions. 

Here we discuss what factors of 26 are, how to find the prime factors of 26 and how to divide 26 into factors by using the division method and the prime factorization method.

factors of 26

What are the Factors of 26?

In other words, the factors of 26 are the numbers that divide 26 exactly without leaving any remainder. To put it another way, the factors of 26 are the numbers that multiply together in pairs and form an original number.

In addition to 1 and the number itself, 26 is made up of multiple factors.

Factors of 26: 1, 2, 13 and 26

Prime Factorization of 26: 2 × 13

Pair Factors of 26

Pair factors are numbers that, when multiplied together, give the original number. According to our discussion above, 26 can have both positive and negative pairs of pair factors. Let’s look at some of those positive factors.

Positive Factors of 26Positive Pair Factors of 26
1 × 26(1, 26)
2 × 13(2, 13)

In the same manner, 26 has negative pair factors:

Negative Factors of 26Negative Pair Factors of 26
-1 × -26(-1, -26)
-2 × -13(-2, -13)
factors of 26

Factors of 26 by Division Method

Two methods can be used to find factors of 26, such as the division method and the prime factorization method. We will first discuss the division method.

Divide the number 26 by 1 to find its factors. Then divide it by successive numbers to find its factors.

  • 26/1 =26 
  • 26/2 = 13 
  • 26/13 = 2 
  • 26/26 = 1 

The number 26 is not divided exactly if we divide it other than 1, 2, 13, and 26. Therefore, the factors of 26 are 1, 2, 13, and 26.

Prime Factorization of 26

Prime factorization is the process of expressing numbers as the product of their prime factors. Here is how to find the prime factors for 26:

Take the pair factor of 26 and write it down as (2, 13)

As each number 2 and 13 is a prime number, the pair factor cannot be further divided. Multiply the two prime factors.

As a result, the prime factors of 26 are written as the product of 2 and 13.

Consequently, the prime factorization of 26 is 2 × 13 or 21 × 131

factors of 26 by prime factorization

Notable:

If either or both of the numbers in the pair are composite numbers, divide the composite numbers into their prime factors and multiply them together.

Examples

Example 1:

Find the common factor between 26 and 13.

Solution:

1, 2, 13, and 26 are the factors of 26.

Factors of 13 = 1 and 13.

Therefore, 13 and 26 have a common factor of 1 and 13.

Example 2:

Calculate the common factors of 26 and 24.

Solution:

Factors of 26 = 1, 2, 13, 26

24 has the factors 1, 2, 3, 4, 6, 8, 12, and 24.

As a result, 26 and 24 have 2 and 1 in common.

Example 3:

What are the common factors of 26 and 52?

Solution:

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

1, 2, 4, 13, 26, and 52 are the factors of 52.

Thus, 1, 2, 13, and 26 are the common factors of 26 and 52. 

Factors of 16

FAQs

How many factors are there in 26?

1, 2, 13, and 26 are the factors of 26. 26 has more than two factors since it is a composite number.

In what way is 26 prime factorized?

Prime factorization of 26 = 2 × 13.

How many positive pair factors does 26 have?

(1, 26) and (2, 13) are the positive pair factors of 26.

What are the negative pair factors of 26?

There are two negative pair factors for 26: (-1, -26) and (-2, -13).

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