Math Tutor Explains: What are the Factors of 257?

As your math tutor, I’m here to guide you through the different types of factors of 257. So, what are the factors of 257?

• Factors of 257: 1, 257

• Sum of Factors of 257: 258

• Negative Factors of 257: -1, -257

• Prime Factors of 257: 1, 257

• Prime Factorization of 257: 257

There are two ways to find the factors of 257: using factor pairs and using prime factorization.

Factor pairs of 257 are any two numbers that, when multiplied together, equal 257. The question I would ask as a math tutor to guide you is: “what two numbers multiplied together equal 257?” Every factor can be paired with another factor and multiplying the two will result in 257.

In this case, we can see that 257 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, 257 only has one factor pair:

(1, 257)

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

(-1, -257)

Prime factorization is when you break down the factors of 257 to just the prime factors and expressing 257 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 257 is a prime number, we can simply state the primary factorization as 257.

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 257.

257 ÷ 257 = 1

If we divide 257 by 257, we simply get 1, which can’t be broken down any further.

So, the prime factorization of 257 is just 257.

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

Factors of 126 - The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45

Factors of 133 - The factors of 133 are 1, 7, 19, 133

Factors of 99 - The factors of 99 are 1, 3, 9, 11, 33, 99