Sum of first 31 odd prime numbers gives a perfect square. In this chapter, we will learn to calculate the factors of 31, prime factors of 31, and factors of 31 in pairs along with solved examples and interactive questions for a better understanding.

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Factors of 31: 1 and 31Prime Factorization of 31: 31 = 311
1.What Are the Factors of 31?
2.How to Calculate the Factors of 31?
3.Factors of 31 by Prime Factorization
4.Factors of 31 in Pairs
5.FAQs on Factors of 31

What Are the Factors of 31?

Factors of 31 are the numbers which, when multiplied together, result in 31. The factors of 31 are 1 and 31. 31 is prime as its divisible by 1 and itself only.

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Tips and Tricks:

1 is the smallest factor of every number.Every number has a minimum of 2 factors, i.e., 1 and the number itself.All the odd numbers never have 2 as one of their factors.

How to Calculate the Factors of 31?

Step 1: Write down the number to be factored, i.e., 31.Step 2: Find the two numbers whose product gives 31.

31 × 1 = 31The other possible product is 1 × 31 = 31. Hence, it can only be factored as 1 and the number itself.

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Hence, the factors of 31 are 1 and 31.

Explore factors using illustrations and interactive examples.

Factors of 31 by Prime Factorization

If the factors of a number are prime numbers, then the factors are said to be prime factors. Prime factorization is the process of writing a number as a product of its prime factors. The factor tree below shows that there is only one prime factor of 31.

The procedure is to divide the given number by prime factors until the quotient is 1. We get the factors of 31 by prime factorization using the following steps:

Step 1: Write the pair of factors, which on multiplication gives the required number. 31 can be factored as a product of 1 and 31.Step 2: See the factors, whether each one of them is prime or not. Here, 31 is a prime numbers and cannot be factored further while 1 is neither a prime nor a composite number.Step 3: Now we find that the prime factorization of 31 is 31. The prime factor of 31 is 31.

Important Notes:

Factors of any number are all the possible numbers it is divisible by. They may be prime numbers or composite numbers.Prime numbers have only 2 factors, i.e., 1 and itself.Factors are never fractions or decimals.Factors can be negative.

Factors of 31 in Pairs

The factors of 31 in pairs are (1, 31) and (-1, -31).

FactorsFactors of 31 in pairs
1 × 31 = 311, 31
-1 × -31 = 31-1, -31

Think Tank:

What are the common factors between a prime number and a composite number?What are the common factors between a prime number and another prime number? Can you find all the numbers having exactly one factor?Is there any counting number having no factor at all?

Example 2: Kate is baking tarts which are to be placed in identical packages for a food carnival. She has to pack them in such a way that each package consists of one each of the two types of tarts she has baked. She makes 62 almond and buckwheat tarts and 31 brown butter apple tarts. What is the highest number of such packages that can she pack the tarts into? 

Solution:

We understand that she has to make packages that include one each of the two types of tarts she has baked. Hence, we need to find the common number that divides both the numbers, 31 and 62.

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Here, 31 and 1 are the common factors and 31 is the greatest common factor. Thus, Kate will pack 31 packages which include both the types of tarts. She will have 1 brown butter apple tart and 2 almond and buckwheat tarts in each of the 31 packages. Hence, Kate will pack the tarts in 31 packages.