Factors of 31

The factors of 31 are the numbers that divide the number 31 exactly without leaving the remainder. The pair factors of 31 can be positive as well as negative, but they cannot be a decimal or fraction. In this article, we are going to learn what are the factors of 31, pair factors and prime factors of 31 and the procedure for finding the factors of 31 using the division method and the prime factorization method.

Table of Contents:

• What are the Factors of 31?
• Pair Factors of 31
• Factors of 31 by Division Method
• Prime Factorization of 31
• Solved Examples
• FAQs

What are the Factors of 31?

The factors of 31 are the numbers that are multiplied in pairs resulting in the original number. In other words, the factors of 31 are the numbers that divide the number 31 exactly without leaving the remainder. As the number 31 is a prime number, it has only two factors, such as one and the number itself. Therefore, the factors of 31 are 1 and 31.

Pair Factors of 31

The pair factors of 31 are the multiplication of pairs of numbers which on multiplication gives the original number 31. Since the number 31 is a prime number, it should have only one pair factor. As discussed above, the pair factors of 31 can be positive or negative pairs. The following are the positive pair factors of 31.

Similarly, the negative pair factors of 31 are given below:

Factors of 31 by Division Method

One of the methods to find the factors of 31 is the division method. In the division method, the factors of 31 can be found by dividing 31 with consecutive integers starting from 1. If the remainder of the division operation is zero, then the number should be a factor of 31. Go through the following steps to find the factors of 31.

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

If we divide 31 by different numbers other than 1 and 31, it leaves the remainder. Hence, the factors of 31 are 1 and 31 only.

Prime Factorization of 31

The prime factorization of 31 is the process of writing the numbers as the product of its prime factors. Now, let us learn how to find the prime factorization of 31.

Step 1: Write down the pair factors of 31.

Step 2: Determine whether the numbers in the pair factors are prime or composite numbers.

• If both numbers are prime numbers, multiply the prime factors directly.
• If one of the numbers in the pair factors is prime and the other number is composite, split the composite numbers into its prime factors and multiply the prime factors together.
• If both the numbers in the pair factors are composite, split both the numbers further into their prime factors.

Now, let us take the pair factor of 31, say (1, 31)

Here, both the numbers in the pair factors are prime numbers, then write the numbers as the product of 1 and 31.

Thus, 31 can be written as 1 × 31.

Therefore, the prime factorization of 31 is 1 × 31 or 31¹.

Video Lesson on Prime Factors

Examples

Example 1:

Find the common factors of 31 and 13.

Solution:

The factors of 31 are 1 and 31

The factors of 13 are 1 and 13

Therefore, the common factor of 31 and 13 is 1.

Example 2:

Find the common factors of 31 and 62.

Solution:

Factors of 31 = 1, 31

Factors of 62 = 1, 2, 31, 62

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

Example 3:

Find the common factors of 31 and 17.

Solution:

The factors of 31 are 1 and 31.

The factors of 17 are 1 and 17.

As both the number 13 and 17 are prime numbers, the factors of 13 and 17 are one and the number itself.

Therefore, the common factor of 13 and 17 is 1.