Math Tutor Explains: What are the Factors of 19?

As your math tutor, I’m here to guide you through the different types of factors of 19. So, what are the factors of 19?

• Factors of 19: 1, 19

• Sum of Factors of 19: 20

• Negative Factors of 19: -1, -19

• Prime Factors of 19: 1, 19

• Prime Factorization of 19: 19

There are two ways to find the factors of 19: using factor pairs and using prime factorization.

Factor pairs of 19 are any two numbers that, when multiplied together, equal 19. The question I would ask as a math tutor to guide you is: “what two numbers multiplied together equal 19?” Every factor can be paired with another factor and multiplying the two will result in 19.

In this case, we can see that 19 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, 19 only has one factor pair:

(1, 19)

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

(-1, -19)

Prime factorization is when you break down the factors of 19 to just the prime factors and expressing 19 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 19 is a prime number, we can simply state the primary factorization as 19.

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 19.

19 ÷ 19 = 1

If we divide 19 by 19, we simply get 1, which can’t be broken down any further.

So, the prime factorization of 19 is just 19.

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

Factors of 120 - The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Factors of 26 - The factors of 26 are 1, 2, 13, 26

Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128

Factors of 15 - The factors of 15 are 1, 3, 5, 15