Divisible vs. Indivisible — What's the Difference?
By Tayyaba Rehman & Urooj Arif — Updated on May 7, 2024
"Divisible" refers to a number that can be divided by another number without leaving a remainder, while "indivisible" describes something that cannot be divided or separated.
Difference Between Divisible and Indivisible
Table of Contents
ADVERTISEMENT
Key Differences
Divisible means that a number can be divided evenly by another number; for example, 10 is divisible by 2 because it results in a whole number without remainder. Conversely, indivisible refers to numbers or objects that cannot be divided evenly, such as 7 being indivisible by 2 because it leaves a remainder.
In mathematics, divisibility is a fundamental concept used to determine the factors of numbers and solve problems involving ratios and fractions. On the other hand, indivisible often appears in contexts beyond mathematics, such as discussions about fundamental particles in physics that cannot be split or concepts in philosophy that are seen as inherently whole.
The divisibility of a number has practical implications in various fields such as cryptography, where large prime numbers (which are indivisible by any number other than one and themselves) play a crucial role. Indivisibility, when applied to objects or concepts, can suggest integrity or inherent unity, which might be philosophical or moral, like the concept of 'indivisible human rights'.
Educational systems emphasize understanding divisibility rules to help students simplify mathematical operations and understand more complex algebraic concepts. Meanwhile, indivisibility in a cultural or social sense can be used to stress the importance of unity and inseparability, such as in the phrase "liberty and justice for all" in a national pledge.
Both terms also carry symbolic meanings: divisibility can symbolize flexibility and adaptability, whereas indivisibility often represents strength and resilience. While the technical meanings are rooted in mathematics, these broader interpretations play a significant role in discourse across disciplines.
ADVERTISEMENT
Comparison Chart
Definition
Can be divided by another number without a remainder.
Cannot be divided by another number without a remainder.
Use in Mathematics
Used to find factors and simplify calculations.
Used to describe prime numbers and fundamental particles.
Symbolic Meaning
Flexibility, adaptability.
Strength, unity, inseparability.
Examples in Numbers
8 is divisible by 2 and 4.
7 is indivisible by 2 and 3.
Broader Implications
Useful in fields like cryptography.
Important in philosophical or moral contexts.
Compare with Definitions
Divisible
Able to be divided without a remainder.
The number 24 is divisible by 3, yielding 8.
Indivisible
Not capable of being divided or separated.
The concept of justice is often seen as indivisible.
Divisible
Characterized by the capability to be evenly separated.
The divisible assets were allocated equally among the heirs.
Indivisible
Characterizing unity or something whole.
The nation was founded on the principle of being indivisible.
Divisible
Used in discussing the division of objects or responsibilities.
Responsibilities are divisible among team members.
Indivisible
Often used metaphorically to express solidarity.
Their bond was indivisible, enduring all challenges.
Divisible
Pertaining to a number that has multiple factors.
Divisible quantities are essential in fractions.
Indivisible
Pertaining to numbers that are prime.
The number 13 is indivisible by any number other than itself and one.
Divisible
Concerning divisibility rules in mathematics.
Knowing which numbers are divisible by 10 speeds up calculations.
Indivisible
Used to describe elements that cannot be further broken down.
An atom was once thought to be indivisible.
Divisible
Capable of being divided
The marine environment is divisible into a number of areas
Indivisible
Incapable of undergoing division.
Divisible
(of a number) containing another number a number of times without a remainder
24 is divisible by 4
Indivisible
(Mathematics) Incapable of being divided without a remainder
The number 15 is indivisible by 7.
Divisible
Capable of being divided, especially with no remainder
15 is divisible by 3 and 5.
Indivisible
Incapable of being divided; atomic.
Divisible
Capable of being divided or split.
Indivisible
(arithmetic) Incapable of being divided by a specific integer without leaving a remainder.
Divisible
(arithmetic) Of an integer, that, when divided by another integer, leaves no remainder.
12 is divisible by 3.
Indivisible
That which cannot be divided or split.
Divisible
Any substance that can be divided.
Indivisible
(geometry) An infinitely small quantity which is assumed to admit of no further division.
Divisible
Capable of being divided or separated.
Extended substance . . . is divisible into parts.
Indivisible
Not divisible; incapable of being divided, separated, or broken; not separable into parts.
Divisible
A divisible substance.
Indivisible
Not capable of exact division, as one quantity by another; incommensurable.
Indivisible
That which is indivisible.
By atom, nobody will imagine we intend to express a perfect indivisible, but only the least sort of natural bodies.
Indivisible
An infinitely small quantity which is assumed to admit of no further division.
Indivisible
Impossible of undergoing division;
An indivisible union of states
One nation indivisible
Common Curiosities
Why is divisibility important in number theory?
Divisibility helps in understanding the properties of numbers, such as identifying primes and solving for factors.
What does divisible mean in mathematics?
In mathematics, divisible means that one number can be divided by another without leaving a remainder.
Can you give an example of an indivisible object?
In physics, an elementary particle like an electron is considered indivisible because it cannot be broken down into smaller parts.
What is meant by indivisible rights?
Indivisible rights are rights that are seen as absolute and cannot be divided or taken away.
Can divisibility impact legal or financial decisions?
Yes, in legal and financial contexts, divisibility can determine how assets or liabilities are split or shared.
What makes a concept indivisible?
A concept is considered indivisible if it inherently exists as a whole, without parts that can be separated or broken down.
Is the term indivisible used outside of mathematics?
Yes, indivisible is also used in philosophical, moral, and social contexts to denote concepts that are considered whole, unified, and inseparable.
How do divisibility rules aid in calculations?
Divisibility rules simplify the process of determining whether one number can be divided by another, facilitating easier computation, especially with large numbers.
How do the concepts of divisible and indivisible relate to everyday life?
These concepts help in organizing tasks, responsibilities, or resources, emphasizing efficiency in the case of divisibility, and unity or integrity in the case of indivisibility.
What are some practical applications of knowing if a number is divisible by another?
This knowledge is used in simplifying fractions, finding common denominators, and even in coding and cryptography.
Share Your Discovery
Previous Comparison
Diorama vs. Panorama
Next Comparison
Theology vs. TheodicyAuthor Spotlight
Written by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
Co-written by
Urooj ArifUrooj is a skilled content writer at Ask Difference, known for her exceptional ability to simplify complex topics into engaging and informative content. With a passion for research and a flair for clear, concise writing, she consistently delivers articles that resonate with our diverse audience.
