Q:

# What are all the multiples of seven?

A:

The multiples of seven are seven, 14, 21, 28, 35, 42, 49 and so on. It is impossible to list all the multiples of seven because for every multiple there is another multiple greater than it. This is an infinite set, so there is no highest multiple of seven.

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Credit: Ivan Bandura CC-BY 2.0

Multiples are obtained by multiplying the same number by numbers in the set of natural numbers. The first multiple of a number is always the number itself, so the first multiple of seven (7 x 1) is seven itself. Multiplying 7 x 2 gives 14, and this is the second multiple of seven. The third multiple of seven is 7 x 3, yielding 21. Similarly, the nth multiple of seven is obtained by calculating 7 x n, where n is a natural number.

Multiples of a number are exactly divisible by the given number. So, 35 is a multiple of seven and when divided by seven, it yields the remainder zero. To find out whether a number is a multiple of seven, it must not leave a remainder when divided by seven. The number 245 is a multiple of seven as it gives zero as the remainder when divided by seven. The quotient in this case is 35.

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