Math Tutor Explains: What are the Factors of 11?

As your math tutor, I’m here to guide you through the different types of factors of 11. So, what are the factors of 11?

• Factors of 11: 1, 11

• Sum of Factors of 11: 12

• Negative Factors of 11: -1, -11

• Prime Factors of 11: 1, 11

• Prime Factorization of 11: 11

There are two ways to find the factors of 11: using factor pairs and using prime factorization.

Factor pairs of 11 are any two numbers that, when multiplied together, equal 11. The question I would ask as a math tutor to guide you is: “what two numbers multiplied together equal 11?” Every factor can be paired with another factor and multiplying the two will result in 11.

In this case, we can see that 11 is a prime number. By definition, a prime number is a number that doesn’t have any other factors other than itself and 1.

So, 11 only has one factor pair:

(1, 11)

If you also consider negative factors, there is also a second factor pair:

(-1, -11)

Prime factorization is when you break down the factors of 11 to just the prime factors and expressing 11 as a product of those prime factors. Let’s go through the process and simplify it like a math tutor would!

In this case, because 11 is a prime number, we can simply state the primary factorization as 11.

For most numbers, we would take the smallest prime factor that is larger than 1 to start to break down the focus number. In this case, the smallest prime factor larger than 1 is 11.

11 ÷ 11 = 1

If we divide 11 by 11, we simply get 1, which can’t be broken down any further.

So, the prime factorization of 11 is just 11.

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 93 - The factors of 93 are 1, 3, 31, 93

Factors of 2 - The factors of 2 are 1, 2

Factors of 29 - The factors of 29 are 1, 29

Factors of 78 - The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78