If a number cannot be divided into equal groups, then it is known as a prime number.

Can you divide 37 into equal groups of 2? equal groups of 3 ? groups of 4?

Let us find an answer to this question.

In this mini-lesson, we will explore the world of prime numbers by finding the answers to the questions like what is a prime number, is 37 a prime number, or if 37 is a composite number etc., with help of solved examples and interactive questions.

**Lesson Plan**

**Is 37 A Prime Number?**

Any number, greater than 1, having only two factors, 1 and the number itself is known as a prime number.

To determine if 37 is a prime number, let us see the factors of 37 by the division method.

\(37 \div 1 = 37 \)

Let us divide

\(37 \div 2 \)

\(37 \div 2\) leaves a remainder similarly any other number will leave a remainder.

We cannot divide 37 with any other natural number as it leaves a remainder and no other number divides 37 completely.

Hence, 37 has only 2 factors 1 and 37. So, 37 is a prime number.

**Is 37 A Composite Number?**

A composite number is a natural number that has more than two factors.

37 is not a composite number as it has only two factors, that is, 1 and 37

**Solved Examples**

Example 1 |

Lucy has to list prime numbers between 37 and 73. Help her list them.

**Solution**

The prime number chart based on Sieve of Eratosthenes algorithm is shown below

From the above list of prime numbers, Lucy listed the following prime numbers between 37 and 73. They are:

41, 43, 47, 53, 59, 61, 67, and 71

She found there were 8 prime numbers between 37 to 73

\(\therefore\) Prime numbers between 37 and 73 are 41, 43, 47, 53, 59, 61, 67, and 71 |

Example 2 |

John has to prove that 1 added or subtracted to 37, makes it a composite number. How will he prove it?

**Solution**

When 1 is added to 37, John will get 38

When 1 is subtracted from 37, he will get 36

36 and 38 are even numbers and they are divisible by 2

Since 36 and 38 are divisible by 2, they have more than 2 factors, and therefore 36 and 38 are not prime numbers.

\(\therefore\) 36 and 38 are composite numbers. |

- A prime number has only two factors.
- A composite number has more than two factors.
- 37 has only two factors, that is, 1 and 37.
- 37 is a prime number.

**Interactive Questions**

**Here are a few activities for you to practice. **

**Select/Type your answer and click the "Check Answer" button to see the result.**

- Find prime numbers from 27 to 77 whose sum of digits is also a prime number.
- Eva said 34 is a prime number. Can you prove her wrong? Can you list all the factors of 34 by prime factorization?

**Let's Summarize**

The mini-lesson targeted the fascinating concept of is 37 a prime number. The math journey around is 37 a prime number starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

**About Cuemath**

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

**Frequently Asked Questions (FAQs)**

## 1. What are co-prime numbers?

It is a set of any two numbers which have only 1 as their common factor. For example, 5 and 6 are co-prime numbers.

## 2. What are the factors of 37?

The factors of 37 are 1 and 37

## 3. Is 37 a prime number? Yes or No?

Yes, 37 is a prime number because it has only two factors, that is, 1 and 37