an integral multiple of

USAGE SUMMARY

The phrase "an integral multiple of" is correct and usable in written English.
It is typically used in mathematical contexts to describe a number that can be expressed as a whole number multiplied by another number. Example: "The number 12 is an integral multiple of 3, as it can be expressed as 3 times 4."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

20 human-written examples

The solutions that can be predicted only by numerical means exhibit period multiplications (i.e., the response has a period that is an integral multiple of the period of the excitation) and chaos.

Journal of Sound and Vibration

But according to quantum mechanics, the orientation angle of a single particle can assume only certain discrete values because the angular momentum of the particle must be an integral multiple of a fundamental unit of angular momentum.

Encyclopedia Britannica

For now the change in ϕB after traversing a closed path is no longer zero or an integral multiple of a constant μ0I but is rather μ0 times the current enclosed in the path and therefore depends on the path chosen.

Encyclopedia Britannica

Expiration date is an integral multiple of the period length.

Journal of Industrial Engineering International

For DFT, f is necessarily an integral multiple of the fundamental frequency.

EURASIP Journal on Audio, Speech, and Music Processing

The fire spacing was set as an integral multiple of the half pool length.

Combustion and Flame

Human-verified similar examples from authoritative sources

Similar Expressions

39 human-written examples

Let be a positive integral multiple of and with, and let (4.16).

Journal of Inequalities and Applications

Let be a primitive Dirichlet's character with odd conductor and let be a odd positive integral multiple of and.

Journal of Inequalities and Applications

If M is C5-smooth and dimM>1, H is of C4 class and independent of time t, then for any τ>0 the corresponding system has an infinite sequence of contractible periodic solutions of periods of integral multiple of τ such that any one of them cannot be obtained from others by iterations or rotations.

Journal of Functional Analysis

All charged matter rays have a charge exactly equal to that of the negative or positive electron or to some integral multiple of that charge.

Encyclopedia Britannica

If we assume the delay equals to integral multiple of T u /K but not integral multiple of T u, which can be represented as τ = mT u /K, m is a positive integer and [m/K] ≠ 0.

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using the phrase "an integral multiple of", ensure the context involves mathematical or quantitative relationships where integer values are important. This is commonly seen in fields like physics, engineering, and computer science.

Common error

Avoid confusing "integral", which refers to integers or whole numbers, with "integrated", which means combined or incorporated. Using the wrong term can lead to misunderstandings, especially in technical writing.

Linguistic Context

The phrase "an integral multiple of" functions as a mathematical descriptor, specifying that a value is the result of multiplying a quantity by an integer. This is evidenced by examples from Ludwig, where the phrase appears predominantly in scientific and technical contexts.

Expression frequency: Common

Frequent in

Science

80%

Encyclopedias

15%

Wiki

5%

Less common in

News & Media

0%

Formal & Business

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, the phrase "an integral multiple of" is a mathematically precise term denoting that a quantity is the product of another quantity and an integer. Ludwig AI confirms its correct usage, particularly in scientific and technical fields. While alternatives like "whole number multiple of" exist, the original phrase is preferred in formal contexts demanding precision. Remember to distinguish "integral" from "integrated" to avoid confusion. As evidenced by Ludwig, this phrase helps in clarifying relationships in scientific contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

integer multiple of

Synonymous with "an integral multiple of", explicitly stating the integer nature.

multiple of an integer

Rephrases the original phrase, keeping the same meaning but altering the word order.

whole number multiple of

Replaces "integral" with "whole number", emphasizing the integer aspect. It can be used to describe similar mathematical relation.

divisible by

Focuses on the divisibility aspect rather than the multiplicative relationship.

expressed as a whole number times

Describes the explicit multiplication by a whole number.

a product of an integer and

Highlights the multiplication operation with an integer.

a factor of

Highlights the factor relationship, indicating that one number divides evenly into another.

an exact divisor of

Emphasizes the exactness of the division, similar to "divisible by".

proportional to a whole number

Indicates a direct proportionality with an integer value.

quantifiable by integers

Suggests that values can be measured in whole number units.

FAQs

How is "an integral multiple of" used in a sentence?

The phrase "an integral multiple of" is used to indicate that one quantity is a whole number times another. For example, "The frequency is "an integral multiple of" the fundamental frequency."

What's a simpler way to say "an integral multiple of"?

Simpler alternatives include "whole number multiple of" or simply "multiple of an integer", depending on the context and desired level of formality.

When is it appropriate to use the term "an integral multiple of"?

Use "an integral multiple of" in contexts where the exact, whole-number relationship between two quantities is important, such as in physics, engineering, and mathematics. This phrase emphasizes precision.

What's the difference between "an integral multiple of" and "a multiple of"?

While "a multiple of" implies that one number is the product of another, "an integral multiple of" specifically indicates that the multiplier is a whole number (integer). This distinction is crucial in contexts demanding precise mathematical relationships.