###### Asked in Math and Arithmetic

Math and Arithmetic

# Are consecutive natural numbers always relatively prime?

## Answer

###### Wiki User

###### September 24, 2009 3:56AM

No. I had this question for homework and looked it up in my math terms book.

## Related Questions

###### Asked in Math and Arithmetic

### Why can't two consecutive whole numbers be prime?

In fact, they can. 2 and 3 are consecutive prime numbers.
For larger numbers, one of two consecutive numbers will always
be even, and therefore, not a prime.
In fact, they can. 2 and 3 are consecutive prime numbers.
For larger numbers, one of two consecutive numbers will always
be even, and therefore, not a prime.
In fact, they can. 2 and 3 are consecutive prime numbers.
For larger numbers, one of two consecutive numbers will always
be even, and therefore, not a prime.
In fact, they can. 2 and 3 are consecutive prime numbers.
For larger numbers, one of two consecutive numbers will always
be even, and therefore, not a prime.

###### Asked in Prime Numbers

### Why 35 and 7 are the only three consecutive odd prime numbers?

If you take three consecutive odd (or three consecutive even)
numbers, one of the three will always be a multiple of 3.
If you take three consecutive odd (or three consecutive even)
numbers, one of the three will always be a multiple of 3.
If you take three consecutive odd (or three consecutive even)
numbers, one of the three will always be a multiple of 3.
If you take three consecutive odd (or three consecutive even)
numbers, one of the three will always be a multiple of 3.

###### Asked in Prime Numbers

### Why are 2 and 3 the only consecutive prime numbers?

And they are the ONLY consecutive prime numbers because if you
have one prime number (i.e. 29), then there always is an even
number right after the prime number (i.e. 30 comes right after 29),
and consecutive means "right next to," right? And we all know that
even numbers can always be divided in half, so 2 and 3 are the only
consecutive prime numbers.

###### Asked in Math and Arithmetic

### The HCF of two consecutive numbers is always?

A factor is a number of which the number being considered is a
multiple. Two consecutive numbers cannot both be multiples of 4,
for instance, as there isn't 3 numbers in between them. They cannot
in fact be multiples of any common number other than 1. Thus the
HCF of two consecutive numbers must always be 1.

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