Factors of 26

The factors of 26 are the numbers that are multiplied in pairs to give the original number 26. The pair factors of 26 can be positive as well as negative. For example, the pair factor of 26 can be (1, 26) as well as (-1, -26). If we multiply -1 and -26, it will result in the original number 26. The factors of 26 can be positive or negative. But it cannot be in decimal or fraction form. In this article, we will discuss what are the factors of 26, pair factors and prime factors of 26 and the method of finding the factors of 26 using the division method and the prime factorization method.

Table of Contents:

• What are the Factors of 26?
• Pair Factors of 26
• Factors of 26 by Division Method
• Prime Factorization of 26
• Solved Examples
• FAQs

What are the Factors of 26?

The factors of 26 are the numbers that divide the number 26 exactly without leaving any remainder. In other words, the factors of 26 are the numbers that are multiplied in pairs and results in an original number. As the number 26 is a composite number, it has more factors other than 1 and the number itself.

Pair Factors of 26

The pair factors of 26 are the numbers in pairs which on multiplication give the original number. As discussed above, the pair factors of 26 can be in positive pairs as well as negative pairs. The following are the positive pair factors of 26.

Similarly, the negative pair factors of 26 are as follows:

Factors of 26 by Division Method

The factors of 26 can be found using two different methods, such as the division method as well as the prime factorization method. First, let us start with discussing the division method.

To find the factors of 26, first, divide the number 26 by 1 and then continue dividing the number 26 with consecutive numbers.

• 26/1 =26 (Factor = 1)
• 26/2 = 13 (Factor = 2)
• 26/13 = 2 (Factor =13)
• 26/26 = 1 (Factor = 26)

If we divide the number 26, other than 1, 2, 13 and 26, the number 26 is not divided exactly and leaves the remainder. Hence, the factors of 26 are 1, 2, 13, and 26.

Prime Factorization of 26

The process of writing the numbers as the product of its prime factors is called the prime factorization method. The process of finding the prime factors of 26 is given below:

Step 1: Write down the number 26 and take the pair factor of 26, say (2, 13)

Step 2: From the pair factor (2, 13), both the numbers 2 and 13 are the prime numbers, and hence it cannot be split further. Now, multiply the prime factors 2 and 13.

Thus, the prime factors of 26 are written as the product of 2 and 13.

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

Note:

If any of the numbers in the pair or both the numbers in the pair are composite numbers, split the composite numbers into their prime factors and multiply the prime factors together.

Video Lesson on Prime Factors

Examples

Example 1:

Find the common factors of 26 and 13.

Solution:

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

The factors of 13 are 1 and 13.

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

Example 2:

Find the common factors of 26 and 24.

Solution:

Factors of 26 = 1, 2, 13, 26

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Therefore, the common factors of 26 and 24 are 1 and 2.

Example 3:

Find the common factors of 26 and 52.

Solution:

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

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

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