Factors of 31 (Positive, Negative & Prime Factors)

 The factors of 31 are the numbers that divide 31 evenly, leaving no remainder.

Learning factors is important in mathematics because we use them to:

  • simplify fractions

  • add and subtract fractions

  • solve number problems

  • understand prime and composite numbers

factors of 31 showing positive factors, negative factors, and prime factorization

What Is a Factor?

A factor is a number that divides another number exactly.

If a number divides 31 without leaving a remainder, it is called a factor of 31.

How to Calculate the Factors of 31

To find the factors of 31, divide 31 by whole numbers and check if the result is also a whole number.

Division method:

  • 31 ÷ 1 = 31

  • 31 ÷ 31 = 1

No other whole numbers divide 31 evenly.

Positive Factors of 31

The positive factors of 31 are:

  • 1 × 31 = 31

  • 31 × 1 = 31

✅ Positive factors:
1, 31

Negative Factors of 31

Negative factors also multiply to give 31.

  • −1 × −31 = 31

  • −31 × −1 = 31

✅ Negative factors:
−1, −31

Prime Factorization of 31

A prime number has only two positive factors: 1 and itself.

Since 31 is divisible only by 1 and 31, it is a prime number.

Prime factorization:

31 = 31 × 1

✅ Prime factor of 31: 31

Summary of Factors of 31

  • Positive factors: 1, 31

  • Negative factors: −1, −31

  • 31 is a prime number

  • Prime factorization: 31 × 1

FAQs About Factors of 31

What are the factors of 31?

The factors of 31 are 1 and 31. These are the only numbers that divide 31 evenly.

Is 31 a prime number?

Yes, 31 is a prime number because it has only two positive factors: 1 and 31.

How many factors does 31 have?

The number 31 has two positive factors and four total factors if negative factors are included.

Are there any composite factors of 31?

No, 31 does not have composite factors because it is a prime number.

Why is 31 used in factor examples?

31 is often used in examples because it is a prime number, which makes it easy to understand how factors work.

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