Math Tutor Explains: What are the Factors of 101?

As your math tutor, I’m here to guide you through the different types of factors of 101. So, what are the factors of 101?

• Factors of 101: 1, 101

• Sum of Factors of 101: 102

• Negative Factors of 101: -1, -101

• Prime Factors of 101: 1, 101

• Prime Factorization of 101: 101

There are two ways to find the factors of 101: using factor pairs and using prime factorization.

Factor pairs of 101 are any two numbers that, when multiplied together, equal 101. The question I would ask as a math tutor to guide you is: “what two numbers multiplied together equal 101?” Every factor can be paired with another factor and multiplying the two will result in 101.

In this case, we can see that 101 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, 101 only has one factor pair:

(1, 101)

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

(-1, -101)

Prime factorization is when you break down the factors of 101 to just the prime factors and expressing 101 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 101 is a prime number, we can simply state the primary factorization as 101.

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 101.

101 ÷ 101 = 1

If we divide 101 by 101, we simply get 1, which can’t be broken down any further.

So, the prime factorization of 101 is just 101.

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

Factors of 147 - The factors of 147 are 1, 3, 7, 21, 49, 147

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

Factors of 49 - The factors of 49 are 1, 7, 49

Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90