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Factors of 31
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What are the Factors of 31?
As your math tutor, I’m here to guide you through the different types of factors of 31. So, what are the factors of 31?
• Factors of 31: 1, 31
• Sum of Factors of 31: 32
• Negative Factors of 31: -1, -31
• Prime Factors of 31: 1, 31
• Prime Factorization of 31: 31
There are two ways to find the factors of 31: using factor pairs and using prime factorization.
The Factor Pairs of 31
Factor pairs of 31 are any two numbers that, when multiplied together, equal 31. The question I would ask as a math tutor to guide you is: “what two numbers multiplied together equal 31?” Every factor can be paired with another factor and multiplying the two will result in 31.
In this case, we can see that 31 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, 31 only has one factor pair:
(1, 31)
If you also consider negative factors, there is also a second factor pair:
(-1, -31)
Prime Factorization of 31
Prime factorization is when you break down the factors of 31 to just the prime factors and expressing 31 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 31 is a prime number, we can simply state the primary factorization as 31.
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 31.
31 ÷ 31 = 1
If we divide 31 by 31, we simply get 1, which can’t be broken down any further.
So, the prime factorization of 31 is just 31.
Math Tutor Suggests: Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
Factors of 105 - The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
Factors of 123 - The factors of 123 are 1, 3, 41, 123
Factors of 109 - The factors of 109 are 1, 109
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