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224 LearnersLast updated on December 6th, 2024
Factors of 1024
What's your say about the factors of 1024? Factors are essentially the numbers that can be multiplied together to give an original number. In other words, finding those perfect pairs that go into making 1024 without leaving a remainder.
What are the factors of 1024?
Similarly, as we learned above, factors of 1024 are such numbers that will be multiplied to get 1024. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.
1024 has only 11 factors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and 1024.
Negative factors of 1024: Negative factors are nothing but the negative counterparts of the position factors of a number.
Since 1024 has 11 positive factors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024, it will also have 11 negative counterparts, which are -1, -2, -4, -8, -16, -32, -64, -128,- 256, -512 and -1024.
Prime factors of 1024: Since 1024 is a composite number, it has 2 as its prime factor.
Prime factorization of 1024: Prime factorization of a number is the method of expressing 1024 as a product of prime factors.
The prime factorization of 1024 = 210
How to find the factors of 1024
There are several ways of finding factors of 1024. We will learn about them one by one as we go on.
Finding factors using multiplication
In this method, we will try to find such a pair of numbers that will give 1024 as their product. We recommend that you should follow the following steps to find factors using multiplication.
Step 1: Always look for a pair of numbers whose product is 1024.
Step 2: After finding such pairs, list them all one by one.
Here, factor pairs of 1024 are (1, 1024), (2, 512), (4, 256), (8, 128), (16, 64), (32, 32)
So the factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024.
Finding factors by division method
In the method, we need to find such numbers that divide 1024 completely without leaving any remainder.
1024/1 = 1024
1024/ 2 = 512
1024/ 4 = 256
1024/ 8 = 128
1024/ 16 = 64
1024/ 32 = 32
1024/ 64 = 16
1024/ 128 = 8
1024/ 256 = 4
1024/ 512= 2
1024/ 1024 = 1
All the 11 numbers: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024 mentioned above divide 1024 completely without any remainder. Hence, they are factors of 1024.
Prime Factors and Prime Factorization
In the prime factorization method, a number is expressed as the product of prime factors.
Here, as we know, 1024 = 210
2 is the prime factor when multiplied 10 times will give 1024 as a product of prime numbers.
Factor tree
A factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
Factor Pairs
The factor pairs of a number refer to a pair of numbers which, when multiplied, will give the number as a product.
The factor pairs of 1024 are
Positive Pair Factors of 1024 are (1, 1024), (2, 512), (4, 256), (8, 128), (16, 64), (32, 32)
Negative Pair Factors of 1024 are (-1, -1024), (-2, -512), (-4, -256), (-8, -128), (-16, -64), (-32, -32)
Common Mistakes and How to Avoid Them in Factors Of 1024
Factors of 1024 examples
Problem 1
Can you prove that 16 is also a factor of 1024 by using the divisibility rule of 2 ?
Explanation
Problem 2
If you have 1024 chocolates, and you have 32 friends to distribute among , how many shall each one get ?
Explanation
Problem 3
How many factors of 1024 are also the factors of 2048?
Explanation
Problem 4
Is there any remainder that gets left behind when 1024 is divided by 8 ?
Explanation
Problem 5
If you have 1024 square stickers, then how can you arrange them to fill up a square wall such that each side of the wall has an equal number of stickers ?
Explanation
FAQs on Factors of 1024
1.Why does 1024 hold special importance in computer applications?
2.What is the sum of all the 11 factors of 1024?
3. Is 1024 a perfect square or a perfect cube?
4.How many bytes make a kilobyte?
5.What is the smallest composite number of 1024?
Important Glossaries for Factors of [Topic]
- Prime Numbers: Those numbers which have no other factors other than 1 & the number itself.
- Composite Numbers: Those numbers that have more than 2 factors.
- Negative Factors: These are the counterparts of the positive factors of a number.
- Prime Factorization: Process of breaking down a composite number into products of several of its prime factors.
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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.
