Math Tutor Explains: What are the Factors of 61?

As your math tutor, I’m here to guide you through the different types of factors of 61. So, what are the factors of 61?

• Factors of 61: 1, 61

• Sum of Factors of 61: 62

• Negative Factors of 61: -1, -61

• Prime Factors of 61: 1, 61

• Prime Factorization of 61: 61

There are two ways to find the factors of 61: using factor pairs and using prime factorization.

Factor pairs of 61 are any two numbers that, when multiplied together, equal 61. The question I would ask as a math tutor to guide you is: “what two numbers multiplied together equal 61?” Every factor can be paired with another factor and multiplying the two will result in 61.

In this case, we can see that 61 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, 61 only has one factor pair:

(1, 61)

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

(-1, -61)

Prime factorization is when you break down the factors of 61 to just the prime factors and expressing 61 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 61 is a prime number, we can simply state the primary factorization as 61.

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 61.

61 ÷ 61 = 1

If we divide 61 by 61, we simply get 1, which can’t be broken down any further.

So, the prime factorization of 61 is just 61.

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

Factors of 131 - The factors of 131 are 1, 131

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

Factors of 143 - The factors of 143 are 1, 11, 13, 143

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