# Factors of 31

Factors of 31 are 1 and 31

#### How to find factors of a number

 1.   Find factors of 31 using Division Method 2.   Find factors of 31 using Prime Factorization 3.   Find factors of 31 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 31

• Divide 31 by 1: 31 ÷ 1 : Remainder = 0
• Divide 31 by 31: 31 ÷ 31 : Remainder = 0

Hence, Factors of 31 are 1 and 31

#### 2. Steps to find factors of 31 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 31 using the division method, follow these steps:

• Step 1. Start dividing 31 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 31, which is 31. Divide 31 by 31 to obtain the quotient (1).
31 ÷ 31 = 1
• Step 3. Repeat step 1 with the obtained quotient (1).

So, the prime factorization of 31 is, 31 = 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 31 as shown below:

So, the prime factorization of 31 is, 31 = 31.

#### 3. Find factors of 31 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 31 would be the two numbers which, when multiplied, give 31 as the result.

The following table represents the calculation of factors of 31 in pairs:

Factor Pair Pair Factorization
1 and 31 1 x 31 = 31

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 31. They are called negative pair factors.

Hence, the negative pairs of 31 would be ( -1 , -31 ) , .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 31 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 31 are exact divisors of 31.
• Factors of 31 are 1, 31. Each factor divides 31 without leaving a remainder.

• Is 31 a perfect square?

No 31 is not a perfect square.

• What are factors of 31?

Factors of 31 are 1, 31.

• Which is greatest factor of 31?

The greatest factor of 31 is 1.

• What is the sum of all factors of 31?

The sum of all factors of 31 is 32.

• What are multiples of 31?

First five multiples of 31 are 62, 93, 124, 155.

• What is the greatest prime factors of 31?

The greatest prime factor of 31 is 31.

• What are six multiples of 31?

First five multiples of 31 are 62, 93, 124, 155, 186, 217.

• What is prime factorization of 31?

Prime factorization of 31 is 31.

• Is 31 a whole number?

Yes 31 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 31? Help her in writing all the factors.

Positive factors are 1, 31.
Negative factors are -1, -31.

Can you help Sammy find out the product of the odd factors of 31?

Factors of 31 are 1, 31.
Odd factors of 31 are 1, 31.
Hence product of odd factors of 31 is; 1 x 31 = 31.

Joey wants to write all the prime factors of 31 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 31 are 31.
So in exponential form it can be written as 31.

How many factors are there for 31?

Factors of 31 are 1, 31.
So there are in total 2 factors.

Kevin has been asked to write 1 factor(s) of 31. Can you predict the answer?

1 factor(s) of 31 is 1.

Sammy is puzzled while calculating the prime factors of 31. Can you help him find them?

Factors of 31 are 1, 31.
Prime factors of 31 are 31

What is prime factorization of 31?

Prime factorization of 31 is 31 = 31.