Multiples of 14

Multiples of a number are the products obtained by multiplying the given number by other natural numbers. We know that every number is a multiple and the factor of itself. Thus, 14 is a factor of 14, and also 14 is a multiple of 14. However, there is a difference between factors and multiples, which you can learn here.

The multiples of 14 are 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, etc. We can observe that it is a sequence where the difference between each next number and the preceding number, i.e. two consecutive multiples or products, is equal to 14.

What are the multiples of 14?

Multiples of 14 are numbers that can be divided by 14 without a remainder. In other words, the multiples for 14 are the numbers that are produced when 14 is multiplied by any natural number. That means any number that can be expressed in 14n where n is an integer is a multiple of 14. So, for example, we have two values, p and q; we say that q is a multiple of p if q = np for some integer n. Thus, finding multiples of 14 is relatively easy.

For example, 70, 126, 168 and 210 are all multiples of 14 for the following reasons.

We can also justify the above numbers using the division method as:

70 ÷ 14 = 5 {remainder = 0}

126 ÷ 14 = 9 {remainder = 0}

168 ÷ 14 = 12 {remainder = 0}

210 ÷ 14 = 15 {remainder = 0}

Thus, the above numbers are multiples of 14.

We can also find the multiples through the repeated addition of a number as many times as required. Let us find the first five multiples of 14 by multiplication and add the number repeatedly, as shown below.

The first multiple of 14 is: 14 × 1 = 14

The second multiple of 14 is: 14 × 2 = 28 Or 14 + 14 = 28 {here 14 is added for twice}

The third multiple of 14 is: 14 × 3 = 42 Or 14 + 14 + 14 = 42 {here 14 is added for thrice}

The fourth multiple of 14 is: 14 × 4 = 56 Or 14 + 14 + 14 + 14 = 56

The fifth multiple of 14 is: 14 × 5 = 70 Or 14 + 14 + 14 + 14 + 14 = 70

In the same way, we can write several multiples of the given numbers.

Multiples of 14 Table

The first 20 Multiples of 14 in order along with the multiplication notation in each case are tabulated below.

The above table is quite similar to the multiplication table of 14 since in both the cases the results are the same.

What is a multiple and factor of 14?

Multiples of a number are the n-times of the given number. However, factors are the numbers which when multiplied together, produce the original number.

A number contains infinite multiples, whereas the number of factors of a number is finite.

The multiples of 14 are 14, 28, 42, 56, 70, 84, etc. The factors of 14 are 1, 2, 7 and 14.

Video Lesson on Common Multiples

Get the Multiples of More Numbers Here

Examples

Example 1:

Find the common multiples of 14 and 21.

Solution:

The multiples of 14 include: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350….

The multiples of 21 are: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420….

Thus, the common multiples of 14 and 21 are 42, 84, 126, 168, 210, 252, 294, 336, etc.

Example 2:

What are the multiples of 14 up to 100?

Solution:

The multiples of 14 up to 100 are 14, 28, 42, 56, 70, 84, and 98.

These can be written as:

14 × 1 = 14

14 × 2 = 28

14 × 3 = 42

14 × 4 = 56

14 × 5 = 70

14 × 6 = 84

14 × 7 = 98