# Factors Of 31 – With Division and Prime Factorization

## Factors Of 31

The factors of 31 are the numbers that divide 31 exactly without leaving a remainder. 31 can have positive and negative pair factors, but they cannot be fractions or decimals.

We will learn factors and prime factors of 31 and how to find the factors of 31 using the division method and prime factorization method.

## What are the Factors of 31?

Factors of 31 are multiplied in pairs to produce the original number. A factor of 31 is a number that divides 31 exactly without leaving a remainder.

Prime numbers such as 31 have only two factors: one and the number. As a result, 31 has two factors, 1 and 31.

Factors of 31: 1 and 31

Prime Factorization of 31 = 1 × 31 or 311

## Factors Of -31

When we multiply two numbers to get the product -31, it comes the following:

-1 x  31 =  -31

1 x -31 =  -31

Therefore,  we have two possible factors of -31 as (-1 x  31) and (1 x -31).

Factors of -31:  -1 and -31

## Pair Factors of 31

Pair factors of 31 result from multiplying two numbers, which, when multiplied, result in the number 31. Prime numbers cannot have more than one pair factor.

As described above, there can be positive or negative pair factors in 31. Here are some positive pair factors of 31.

As well, the negative pair factors for 31 are given below:

## Factors of 31 by Division Method

The division is one of the methods for finding the factors of 31. Divide 31 by consecutive integers starting at 1 to find the factors of 31 using the division method.

A factor of 31 should result from a division operation with zero remainders. Follow these steps to find the factors of 31.

• 31/1 = 31   (Factor 1 and Remainder 0)
• 31/31 = 1   (Factor 31 and Remainder 0)

When we divide 31 by a number other than 1 and 31, it leaves a remainder. This means that 31 has only two factors: 1 and 31.

## Prime Factorization of 31

A prime factorization of 31 is writing the number as a product of its prime factors. Now let’s figure out how to find the prime factorization of 31.

Take a note of the pair factors of 31.

Analyze the pair factors to determine whether they are composite or prime.

• Multiply the prime factors directly if both numbers are prime numbers.
• Divide the composite number into its prime factors and multiply the prime factors if one of the numbers is prime and the other is composite.
• In the case of composite factors, split both numbers into their prime factors.

Let us now consider the pair factor of 31 (1, 31).

Since both factors in this pair are prime numbers, we write the numbers as the product of 1 and 31.

Therefore, 31 can be written as 1 × 31.

This means that the prime factorization of 31 is 1 x 31 = 311.

## Examples

Example 1:

What are the common factors of 31 and 13?

Solution:

1 and 31 are the factors of 31

1 and 13 are the factors of 13

Therefore, 31 and 13 have a common factor of 1.

Example 2:

Find the common factor between 31 and 62.

Solution:

Factors of 31 = 1 and 31

1, 2, 31, 62 are the factors of 62

1 and 31 are the common factors of 31 and 62.

Example 3:

What are the common factors of 31 and 17?

Solution:

31 has two factors, 1 and 31.

1 and 17 are the factors of 17.

Because 13 and 17 are prime numbers, their factors are the number Itself and 1.

Therefore, 13 and 17 have a common factor of 1.

## FAQs

### How many factors are there in 31?

The factors of 31 are 1 and 31 because 31 is a prime number.

### What is the prime factorization of 31?

Prime factorization of 31 is 1 × 31 or 311.

### How many positive and negative pair factors does 31 have?

(1, 31) and (-1, -31), respectively, are the positive and negative pair factors of 31.

### Is 2 a factor of 31?

Two is not a factor of 31. By dividing 31 by 2, we get 1 as the remainder, so 2 is not a factor of 31.