101 LearnersLast updated on May 26th, 2025
Factors of -64
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of -64, how they are used in real life, and tips to learn them quickly.
What are the Factors of -64?
The numbers that divide -64 evenly are known as factors of -64.
A factor of -64 is a number that divides the number without remainder.
The factors of -64 are 1, 2, 4, 8, 16, 32, and 64.
Negative factors of -64: -1, -2, -4, -8, -16, -32, and -64.
Prime factors of -64: 2.
Prime factorization of -64: 26.
The sum of factors of -64: 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127
How to Find Factors of -64?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give -64. Identifying the numbers which are multiplied to get the number -64 is the multiplication method.
Step 1: Multiply -64 by 1, -64 × 1 = -64.
Step 2: Check for other numbers that give -64 after multiplying
-1 × 64 = -64
-2 × 32 = -64
-4 × 16 = -64
-8 × 8 = -64
Therefore, the positive factor pairs of -64 are: (1, -64), (2, -32), (4, -16), and (8, -8).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide -64 by 1, -64 ÷ 1 = -64.
Step 2: Continue dividing -64 by the numbers until the remainder becomes 0.
-64 ÷ 1 = -64
-64 ÷ 2 = -32
-64 ÷ 4 = -16
-64 ÷ 8 = -8
Therefore, the factors of -64 are: 1, 2, 4, 8, 16, 32, 64.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of -64 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-64 ÷ 2 = -32
-32 ÷ 2 = -16
-16 ÷ 2 = -
8 -8 ÷ 2 = -4
-4 ÷ 2 = -2
-2 ÷ 2 = -1
The prime factor of -64 is 2. The prime factorization of -64 is: 2^6.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, -64 is divided by 2 to get -32.
Step 2: Now divide -32 by 2 to get -16.
Step 3: Then divide -16 by 2 to get -8.
Step 4: Divide -8 by 2 to get -4.
Step 5: Divide -4 by 2 to get -2.
Step 6: Finally, divide -2 by 2 to get -1. Here, the division process ends as we reach -1.
So, the prime factorization of -64 is: 26.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of -64: (1, -64), (2, -32), (4, -16), and (8, -8).
Negative factor pairs of -64: (-1, 64), (-2, 32), (-4, 16), and (-8, 8).
Common Mistakes and How to Avoid Them in Factors of -64
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every word. Always remember to include 1 and the number itself.
For example, in factors of -64, 1 and -64 is also a factor.
Factors of -64 Examples
Problem 1
A library has -64 old books to dispose of. If they distribute them equally among 8 charities, how many books will each charity receive?
Each charity will receive -8 books.
Explanation
To distribute the books equally, we need to divide the total books by the number of charities.
-64/8 = -8
Problem 2
A storage facility has a negative balance of -64 items due to returns. If each crate holds 16 items, how many crates will be filled?
4 crates.
Explanation
To find the number of crates, we use the formula, Total items = crates × items per crate -64 = crates × 16
To find the number of crates, divide the total items by the items per crate.
-64/16 = -4
Problem 3
A company has -64 defective products. If each box contains 32 products, how many boxes are there?
There are -2 boxes.
Explanation
To find the number of boxes, divide the total defective products by products per box.
-64/32 = -2
Problem 4
A batch of -64 components needs to be reprocessed. If each worker handles 4 components, how many workers are required?
16 workers.
Explanation
Dividing the components by the components handled by each worker, we will get the number of workers.
-64/4 = -16
Problem 5
A manufacturer needs to remove -64 faulty parts from inventory. If each removal unit processes 2 parts, how many units are needed?
32 units.
Explanation
Divide total faulty parts by parts per unit.
-64/2 = -32
FAQs on Factors of -64
1.What are the factors of -64?
2.Mention the prime factors of -64.
3.Is -64 a multiple of 8?
4.Mention the factor pairs of -64?
5.What is the cube of -64?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of -64?
7.What are some fun ways kids in United Arab Emirates can practice Factors of -64 with numbers?
8.What role do numbers and Factors of -64 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of -64 skills?
Important Glossaries for Factors of -64
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -64 are 1, 2, 4, 8, 16, 32, 64.
- Prime factors: The factors which are prime numbers. For example, 2 is a prime factor of -64.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of -64 are (1, -64), (2, -32), etc.
- Negative factors: These are the factors of a number that are negative. For example, -1, -2, -4 are negative factors of -64.
- Prime factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of -64 is 26.
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About BrightChamps in United Arab Emirates
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
