**Factors of 31 are 1, 31**.

Here is complete detailed methods to find the factors of 31.

Actually, Factor is a number which divides any number completely without leaving remainder.

Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then the numbers that we multiply, are the factors of the product.

For example, if we multiply 1 to 31, it gives 31. Here 1 and 31 are called positive factors and if we multiply -1 to -31, it gives 31. So -1 and -31 are called negative factors.

Table of Contents

## How to Find The Factors of 31 ?

Since factors of 31 are the numbers, which divides 31 completely without leaving remainder. So here we are going to divide 31 by all numbers up to 31. Let’s see the process –

We have to stop the process, if any number of column ‘B’ appears in column ‘A’ or when any element comes in both columns at same level and this element will consider as a factor.

Here we stop the division when 31 appears in column ‘A’, which has already been came in column ‘B’.

Hence, all the factor of 31 in above table are : 1, 31

Similarly, negative factor of 31 are : -1, -31

## What Are The Factors of 31 in Pairs ?

As we saw in above table, 1 multiply by 31 gives 31. So (1, 31) is a factor pair of 31. Let us see how many factor pairs can be achieved –

1 x 31 = 31

31 x 1 = 31

Similarly, negative factor pairs of 31 can be written as follows –

-1 x -31 = 31

-31 x -1 = 31

Hence, 31 has 2 factor pairs.

## What Are the Prime Factors of 31 ?

Since 31 is itself a prime number, hence it has only one prime factor i.e. 31. Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.

- Division Method
- Factor Tree Method

### Prime Factors of 31 by Division Method

**Step 1 :** Divide the number by the smallest prime number, which divides the number exactly.**Step 2 :** Divide the quotient again by the smallest prime number. If quotient is not exactly divisible by the

smallest prime number, choose next smallest prime number.**Step 3 :** Repeat Step 2 again and again till the quotient becomes 1.**Step 4 :** All the prime numbers used in above process are the prime factors.

Check : Multiply all the prime factors, the multiplication should be the number itself.

Caution : In this method, only prime numbers will be use to divide.

Since 31 is a prime number, hence 31 has only one prime factor i.e. 31.

### Factor Tree of 31

**Step 1 :** Write a number as root of the tree**Step 2 :** Find the factors of the number, each factor will be considered as root again (now, we got 2 new root)**Step 3 :** Repeat step 2 until we can’t factor any more (or until we got prime factor)**Step 4 :** The end nodes are the prime factors.

We can initiate the tree by choosing any two factors. Here we choose 1 and 31 as factors of 31.

We got the same unique nodes in every tree.

The Factor Tree may be made so many types depends upon choosing the initial and middle factors.

## Number of Factors of 31

The **Number of Factors of 31 is **2.

If we consider both positive and negative factors, then

total no. of factors = 2 (positive) + 2 (negative) = 4

I hope, this step-by-step tutorial will be helpful to understand factorization method of 31.

## FAQ

### What are the factors or divisors of the number 31?

The factors or divisors of the number 31 are 1, 31.

### What are the prime factors of the number 31?

The prime factors of the number 31 is only 31 as it is a prime number itself.

### What is the total number of factors of the number 31?

The total number of factors of the number 31 is 2.

### What is the total number of prime factors of the number 31?

The total number of prime factors of the number 31 is 1.

### What is the sum of all factors of the number 31 including 31?

The sum of all the factors of the number 31 including 31 is 40 (i.e 1 + 31 = 40)

### What is the sum of all factors of the number 31 excluding 31?

The sum of all the factors of the number 31 excluding 31 is 1.

### What are the factor combinations of the number 31?

The factor combinations of the number 31 are (1, 31) & (31, 1).

### What is the prime factorization of the number 31?

The prime factorization of the number 31 is 31.

### What is the product of all factors of the number 31?

The product of all factors of number 31 is 31 (i.e. 1 x 31 = 31)

### What is the product of all prime factors of the number 31?

The product of all prime factors of number 31 is 31.

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