Multiples of 3: Calculation and Sample Questions

Multiple is a product formed by multiplying one number by another. Multiples of 3 are numbers that can be evenly divided by 3.

• For instance if one says 3*5 = 15, 15 is a multiple of 3 and 5. 
• Other multiples of 3 include 3(3*1 = 3), 6 (3*2 = 6), 12 (4*3 = 12), and so on.

Read More: Highest Common Factor

Key Terms: Factors, Multiples, Prime Numbers, Number of Factors, Number of Multiples, Prime factorization, Integers.

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Multiples of 3

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When a number is multiplied by an integer, a multiple is formed. When an integer is multiplied by 3, the results are multiples of 3. There are both odd and even multiples of 3. The odd multiples of three are 3, 9, 15, and so forth, which are not divisible by 2, while the even multiples of 3 are 6, 12, 18, and so forth, which are divisible by 2. 

• The first 5 Multiples of 3 are 3, 6, 9, 12, and 15.
• prime factors of 3 : 3 = 3¹

Read More: Properties of Real Numbers

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Set of Multiples of 3

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Multiples of three can be written in the roster or tabular form, as well as in the inset builder.

• The set numbers are written within brackets separated by commas in the roster or tabular form, therefore multiples of three are expressed as

{0, 3, 6, 9, 12,...}

• Elements of a set are written with their properties in the Inset Builder form, thus Multiples of 3 will be represented as

{x:x = 3n, n W, where W is an integer.}

Read More: Difference Between Fraction and Rational Numbers

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Difference between Factors and Multiples

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The precise divisors of the provided number can be described as its factors, whereas the multiples of the number are the results of multiplying the given number by other integers.

• Any given number has a finite number of factors, but an infinite number of multiplicands.
• While multiplication is the operation used to find multiples of a given number, division is the operation used to find any number's factors.
• Any given number's result or outcome from its factors will almost always be smaller than or equal to that number, whereas the result or outcome from its multiples should be bigger than or equal to that number.

Now consider the following example:

3 × 4 = 12

In this case, the factors of 12 are 3 and 4.

12 is greater than 3 and 4.

One can therefore deduce the following if X and Y are two numbers and:

If X divides Y, then X is a factor of Y.

If Y is divisible by X, then Y is a multiple of X.

Every number is divisible by 1 and is a multiple of 1, and we are aware that the number divides every integer, making it the common factor of all integers.

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Calculation of Multiples of 3

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Integers can be multiplied to find multiples of the number 3. 

• For example, to compute the Multiples of 3, one will multiply 3 by the natural numbers 1, 2, 3,...... and get 3 x 1, 3 x 2, 3 x 3, 3 x 4, 3 x 5, and so on, which equal 3, 6, 9, 12, 15, and so on. 
• All of the Multiples of 3 in the table of threes are Multiples of threes, i.e. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...... 
• Thus, multiples of 3 are written as 3p, where p is an integer.

Read More: Fractions

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First 15 Multiples of 3

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Also Read:

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Things To Remember

• When one multiplies two numbers, we obtain multiples.
• Each and every number has multiples of itself.
• For any given number, there are an infinite number of multiples.
• The number is always equal to or greater than a multiple of the provided number.
• 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the first ten multiples of three.
• Any given number has a finite number of factors, but an infinite number of multiplicands.
• While multiplication is the operation used to find multiples of a given number, division is the operation used to find any number's factors.