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Factors of 26

Factors of 26 are numbers that, when multiplied in pairs give the product as 26. There are overall 4 factors of 26 among which 26 is the biggest factor and its positive factors are 1, 2, 13 and 26. The sum of all factors of 26 is 42 and its factors in Pairs are (1, 26) and (2, 13).

Factors of 26: 1, 2, 13 and 26
Negative Factors of 26: -1, -2, -13 and -26
Prime Factors of 26: 2, 13
Prime Factorization of 26: 2 × 13 = 2 × 13
Sum of Factors of 26: 42

1.	What Are the Factors of 26?
2.	How to Calculate Factors of 26?
3.	Prime Factorization of 26
4.	Factors of 26 in pairs
5.	FAQs on Factors of 26
6.	Challenging Questions

What are the Factors of 26?

Factors of 26 are the numbers which when multiplied together result in 26. The number 26 is not a prime number. Being a composite number, 26 has more than two factors.

factors of 26 in the form of product

Explore factors using illustrations and interactive examples

Factors of 27: The factors of 27 are 1, 3, 9 and 27.
Factors of 81: The factors of 15 are 1, 3, 9, 27 and 81.
Factors of 16: The factors of 16 are 1, 2, 4, 8 and 16.
Factors of 28: The factors of 28 are 1, 2, 4, 7, 14 and 28.
Factors of 25: The factors of 25 are 1, 5 and 25

How to Calculate the Factors of 26?

We can calculate the factors of a number in two ways, either by division method or by prime factorization. Let's begin calculating the factors of 26 by the division method, starting with the whole number 1.

26 ÷ 1 = 26 and remainder is 0.
26 ÷ 2 = 13 and remainder is 0.
26 ÷ 13 = 2 and remainder is 0.
26 ÷ 26 = 1 and remainder is 0.

Thus we find 26 is not divisible by any other number. We have obtained factors 1, 2, 13, 26.

Factors of 26 by Prime Factorization

Prime factorization means to express a composite number as the product of its prime factors.

To get the prime factorization of 26, we divide it by its smallest prime factor which is 2. 26 ÷ 2 = 13.
Since 13 is a prime number, it is divisible by 13 only.
This process goes on till we get the quotient as 1. There are no further prime factors of 26.

prime factorization of 26

The prime factorization of 26 = 2 × 13.

Factors of 26 in Pairs

The pair of numbers which gives 26 when multiplied is known as factor pairs of 26. The following are the factors of 26 in pairs.

factors of 26 in pairs

Thus we have (1,26) ; (2,13) (-1,-26) and (-2,-13) as factors of 26 in pairs.

Important Notes

26 has more than two factors and thus it is a composite number.
26 is a non-perfect square number. Thus, it has an even number of factors. This property holds true for every non-perfect square number.
Factors are never fractions or decimals.

Challenging Questions

Using the prime factorization method, prove that 13 is a prime number.

Factors of 26 Solved Examples

Example 1: Ms. Silvia has a class of 26 students. She wants to divide her class into groups and give them math practice. In how many ways, she can group 26 students so that:
- A group cannot have 1 or all students of the class.
- Each group has an equal number of students.
Solution:

We already learned that the factors of 26 are 1, 2, and 13

But the groups cannot have one or all students. So we ignore 1 and 26

Thus, she can only group them in 1 way with 13 students in each group. And she can make 2 groups.
Example 2: Jack needs to ship 26 spiral notepads and 39 usual notepads. He can pack only one type of notepad in each box. Also, he must pack the same number of notepads in each box. What is the number of notepads Jack can pack in each box?

Solution:

We are already familiar with the ways of finding factors.

The factors of 26 are 1, 2, and 13

The factors of 39 are 1, 3, and 13

The factors that are common to both 13 and 26 are 1 and 13

Therefore, Jack can pack either 1 or 13 notepads in a box.
Example 3: Find the product of all the prime factors of 26.

Solution:

Since, the prime factors of 26 are 2, 13. Therefore, the product of prime factors = 2 × 13 = 26.

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FAQs on Factors of 26

What are the Factors of 26?

The factors of 26 are 1, 2, 13, 26 and its negative factors are -1, -2, -13, -26.

What is the Greatest Common Factor of 26 and 13?

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

Common factors of 26 and 13 are [1, 13].

Hence, the GCF of 26 and 13 is 13.

What are the Pair Factors of 26?

The pair factors of 26 are (1, 26), (2, 13).

How Many Factors of 26 are also common to the Factors of 18?

Since, the factors of 26 are 1, 2, 13, 26 and the factors of 18 are 1, 2, 3, 6, 9, 18.
Hence, [1, 2] are the common factors of 26 and 18.

What is the Sum of the Factors of 26?

Factors of 26 are 1, 2, 13, 26 and, the sum of all these factors is 1 + 2 + 13 + 26 = 42

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