Is 1 a multiple of a number?

Welcome to the site, Donna. I hope you find my answer helpful to your situation. Please let us know if there's another aspect of the situation you'd like to think about with our help.

Test question: "17 is a multiple of only two numbers, 1 and 17. Tell why this statement is true."

I think they are asking the student to show that 17 is not a multiple of any other numbers. To do so, one can show that dividing by 2,3, ... always leaves a remainder.

I think you are asking whether it is right to conclude that "every number must be a multiple of 1 since 1 is a factor of every number".

Yes, every whole number is a multiple of 1. We say that b is a multiple of a when a*n = b (where n is a whole number). Since 1*b = b, for any number b, all numbers are multiples of 1.

It sounds like you also want to double-check your understanding of the two words, 'factor' and 'multiple'. If b is a multiple of a, then a is a factor of b. The two terms describe the same situation from different perspectives.

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Multiples of 1

Methods

Methods for Finding Multiples:

For a beginner, you can find the multiples of a number by skip-counting to the next number. For Instance, if you want to find the multiples of 1, you could start at 1, and keep adding 1 over and over: 1, 2, 3, 4, and so on. Each of these numbers is a multiple of 1. Typically, this works best only for smaller numbers, as adding larger numbers together over and over can be difficult.

Another way to do this is to use multiplication. To find the first few multiples of 1, you could just multiply 1 by each number in sequence, first multiplying by 1, then 2, then 3, and so on, which we will outline below.

What are the Multiples of 1?

So, what are the multiples of 1? Let’s write it out using the multiplication method:

1×1=1 1 × 1 = 1

1×2=21 × 2 = 2

1×3=31 × 3 = 3

1×4=41 × 4 = 4

1×5=51 × 5 = 5

1×6= 61 × 6 = 6

1×7=71 × 7 = 7

1×8=81 × 8 = 8

1×9=91 × 9 = 9

1×10=101 × 10 = 10

So, the first 10 multiples of 1 are: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

There are an endless number of multiples of 1. You could choose any number to multiply by 1 to find a new multiple!

Interesting Facts about Multiples

• Every number is considered the smallest multiple of itself.

• A multiple of a number is very often also the multiple of another number. This is because if you multiply two numbers together, the result is a multiple of both numbers.

• All multiples of even numbers are even.

• The multiples of odd numbers, in sequence, alternate between odd and even numbers.

• You can also find the negative multiples of a number by multiplying by negative numbers.

Practice Finding Multiples of Other Numbers

Finding multiples of any number can be done using the same methods as outlined above. You can see how this can be done with specific numbers, like the ones below, by clicking on the any of the links below:

Multiples of 426 - The first five multiples of 426 are 426, 852, 1278, 1704, 2130

Multiples of 958 - The first five multiples of 958 are 958, 1916, 2874, 3832, 4790

Multiples of 848 - The first five multiples of 848 are 848, 1696, 2544, 3392, 4240

Multiples of 821 - The first five multiples of 821 are 821, 1642, 2463, 3284, 4105

Multiples of 992 - The first five multiples of 992 are 992, 1984, 2976, 3968, 4960

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