Math Tutor Explains: What are the Factors of 401?

As your math tutor, I’m here to guide you through the different types of factors of 401. So, what are the factors of 401?

• Factors of 401: 1, 401

• Sum of Factors of 401: 402

• Negative Factors of 401: -1, -401

• Prime Factors of 401: 1, 401

• Prime Factorization of 401: 401

There are two ways to find the factors of 401: using factor pairs and using prime factorization.

Factor pairs of 401 are any two numbers that, when multiplied together, equal 401. The question I would ask as a math tutor to guide you is: “what two numbers multiplied together equal 401?” Every factor can be paired with another factor and multiplying the two will result in 401.

In this case, we can see that 401 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, 401 only has one factor pair:

(1, 401)

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

(-1, -401)

Prime factorization is when you break down the factors of 401 to just the prime factors and expressing 401 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 401 is a prime number, we can simply state the primary factorization as 401.

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 401.

401 ÷ 401 = 1

If we divide 401 by 401, we simply get 1, which can’t be broken down any further.

So, the prime factorization of 401 is just 401.

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

Factors of 76 - The factors of 76 are 1, 2, 4, 19, 38, 76

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

Factors of 47 - The factors of 47 are 1, 47

Factors of 22 - The factors of 22 are 1, 2, 11, 22