223 LearnersLast updated on May 26th, 2025
Factors of 864
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 864 is not an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!
What are the factors of 864?
Factors are whole numbers that, when multiplied, the product is equal to 864.
864 is not a prime number, its only factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. For every factor, there is not a corresponding negative factor, for 864, the negative factors are -1,-2,-4,-8,-16,-31,-62,-124,-248,-864.
How to find the factors of 864?
There are various methods we apply to find the factors of any number. Few of them are listed here; multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !
Finding Factors Using Multiplication
Step 1: Find all pairs of numbers whose product is 864.
Step 2: All the pairs found represent the factors of 864.
864 is not a prime number. The pair of numbers whose product is 864 is
1×864=864
2×432=864
3×288=864
4×216=864
6×144=864
8×108=864
9×96=864
12×72=864
16×54=864
18×48=864
24×36=864
27×32=864
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864.
Finding Factors by Division Method
Step 1: Start by dividing 864 with the smallest number, and check the remainders.
Step 2: 864 is prime, therefore the only divisors it has are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
Prime factors and prime factorization
— 864 is not a prime number.
— The prime factorization of 864 is 25×33. 2 and 31 are prime factors of 864.
— Factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
Factor tree
— In this method, we make branches that extend from the number to express a number as the product of its factors.
— In case of 864, first branch will be — 2×432 → 2×216 → 2×108 → 2×54 → 2×27 → 3×9 → 3×3 → 3×1. — the factorization ends with 1.
Common mistakes and how to avoid them in factors of 864
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 864. Don’t worry, it is not a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them.
Mistake 1
Excluding negative factors
Every positive factor has a corresponding negative factor. Often times, the negative factors are not included.
Factors of 864 Examples
Problem 1
Find the greatest common factor of 864 and 432.
List the factors of both numbers:
Factors of 864: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864.
Factors of 432: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432.
Identify the largest common factor: 432.
Explanation
The GCF is the largest number that divides both 864 and 432 without any remainder. Listing the factors of each number and finding the biggest match between them gives us the GCF.
Problem 2
What is the product of the smallest and largest factor of 864?
Identify the smallest and largest factors of 864:
Smallest factor: 1.
Largest factor: 864.
Multiply them together: 1×864=864
Explanation
For any number, the smallest factor is always 1, and the largest factor is the number itself. Multiplying these two give us the number, 864.
Problem 3
What are the common factors of 864 and 120?
List the factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
List the factors of 864 (from earlier): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, and 864.
Find the common factors: 1, 2, 3, 4, 6, 8, 12, and 24.
Explanation
We list the factors of both numbers and identify the common ones. These shared factors help us find numbers that divide evenly into both 120 and 864.
FAQs on Factors of 864
1.What is the number of divisors of 864?
2.Is 864 divisible by 3?
3.Is 864 a perfect cube?
4.What is the smallest number that divides into 864?
5.What is the prime factorization of 8649?
Important Glossaries for Factors of 864
- Factors: numbers that divide the given number without leaving a remainder.
- Prime factorization: breaking numbers down into their prime factors.
- Prime factors: Prime numbers that multiply together to form a given number.
- Composite number: Number that has at least more than one divisor other than 1 and the number itself.
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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.
