Let us explore a few facts about the number 64

The number of chequered boxes on a chessboard is 64. In all our computers you can quite often find a 64-bit operating system.

Also, 64 is the first natural number, which can be both written as a square and as a cube.

With this information, let's move ahead to explore the prime factorization 64

In this mini-lesson, we shall explore the prime factorization of 64,* *by finding answers to questions like what is prime factorization of 64, and what are the methods of prime factorization to find the factors of 64

**Lesson Plan**

**What is the prime factorization of 64?**

The number 64 can be expressed as a product of prime factors.

\[\begin{align} 64 &= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\ 64 &= 2^6 \end{align} \]

The various combination of prime numbers results in new factors. The factors of 64 are 1, 2, 4, 8, 16, 32, and 64

Also 64 can be expressed as: \( 64 = 8^2 = 4^3 = 2^6\)

Let us get to know a few details about prime numbers.

- 1 is neither a prime number nor a composite number.
- 2 is the only even prime number., and is the factor of any even number.
- A prime number has only two factors, one and itself.
- There are 25 prime numbers between 1 and 100. \(2\), \(3\), \(5\), \(7\), \(11\), \(13\), \(17\), \(19\), \(23\), \(29\), \(31\), \(37\), \(41\), \(43\), \(47\), \(53\), \(59\), \(61\), \(67\), \(71\), \(73\), \(79\), \(83\), \(89\), \(97\)

**What are the methods of prime factorization to find the factors of 64?**

The prime factors of 64 can be found by the factor tree method and by the long division method.

The non-prime factors of 64 are 32, 16, 8, and 4

Further, the factorization of 64 is possible through the division method.

Let us look at the below steps to find the prime factors by division method.

- A divisor is a prime number and it divides the given number exactly.
- The quotient at each step is sequentially divided again with a prime number.
- The division method concludes with the final quotient as 1

Express 240 as the product of prime factors. Also, list the non-prime factors of the number 240.

**Solved Examples**

Example 1 |

What is the total number of different rectangles which Sam can build, such that its area is equal to 64 square units?

**Solution**

Sam needs to build rectangles of different dimensions and all those rectangles need to have the same area of 64 square units.

This is possible with the various combinations of factors of 64,

The factors of 64 are 1, 2, 4, 8, 16, 32, and 64

Combination - I = \( 1 \times 64 \)

Combination - II = \(2 \times 32\)

Combination - III = \( 4 \times 16 \)

Combination - IV = \( 8 \times 8 \)

\(\therefore\) A total of 4 different rectangles can be constructed. |

Example 2 |

Johnson has a book with 512 pages and each chapter has 8 pages. How many chapters are there in the book?

**Solution**

Total number of pages in the book = 512

Number of pages for each chapter = 8

Total number of chapters = \(\frac{Number~of~pages~in~the~book}{Number~of~pages~in~each~chapter}\)

= \(\frac {512}{8} \)

= 64

\(\therefore\) There are 64 pages in the book |

Example 3 |

Help Daniel to find the common factor of 100 and 64

**Solution**

The first step is to find the factors of 100 and 64

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100

The factors of 64 are 1, 2, 4, 8, 16, 32, 64

Venn Diagram

Of these factors, numbers 1 and 4 are common factors.

Additionally, 4 is called the Greatest Common Factor(GCF) of 100 and 64

\(\therefore\) The numbers 1 and 4 are the common factors of 100 and 64 |

Example 4 |

Gabriel has a list of 60 invitees for a party. For the party, the seating arrangement has to be made such that there are 16 chairs in each row. Find the number of rows and also the total chairs required?

**Solution**

Number of invitees for the party = 60

Number of chairs in each row = 16

The number of chairs required should be equal to or greater than the number 60

Hence the multiple of 16, which is greater than 60 is 64

Total number of chairs required = 64

Number of rows = \(\frac{Total~chairs}{Chairs~in~each~row}\)

= \(\frac{64}{16}\)

= 4

\(\therefore\) A total of 64 chairs are required, and there are 4 rows of chairs. |

**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.**

**Let's Summarize**

The mini-lesson targeted the fascinating concept of prime factorization of 64. The math journey around prime factorization of 64 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 is the factor tree of 64?

The factors of 64 can be found by the factor tree method.

The factors of 64 are 1, 2, 4, 8, 16, 32, and 64

## 2. How do you find the prime factorization?

The division method is used for the prime factorization of a number. The prime factorization of 72 is as follows.

\(72 = 2 \times 2 \times 2 \times 3 \times 3\)

\(72 = 2^3 \times 3^2\)

Similary the prime factorization of 18 is:

\(\begin{align} 18 &= 2 \times 3 \times 3 \\ 18 &= 2^1 \times 3^2 \end{align} \)

The prime factorization of 100 is:

\(\begin{align} 100 &= 2 \times 2 \times 5 \times 5 \\ 100 &= 2^2 \times 5^2 \end{align} \)

## 3. What is the largest factor of 64?

The largest factor of any number is the number itself.

Therefore the largest factor of 64 is 64

## 4. What is the prime factorization of 60?

The prime factorization of 60 is as follows.

\(60 = 2 \times 2 \times 3 \times 5 \)

\(60 = 2^2 \times 3^1 \times 5^1 \)