Question

Which of these are not coprime numbers - (1) `32,24`; (2) `25,32`; (3) `15,22` and (4) `18,35`?

Answer 1

`32` and `24` are not coprime numbers. Hence answer is (1).

Explanation:

Coprime numbers are those numbers, who do not have any factor, other than `1`, common between them. In other words, two numbers are coprime if their GCF is `1`. As we may see below, this may happen even if two numbers are composite.

(2) Factors of `25` and `32` are `25=5xx5` and `32=2xx2xx2xx2xx2`, as there is no common factor, they are coprime numbers.

(3) Factors of `15` and `22` are `15=3xx5` and `22=2xx11`, as there is no common factor, they are coprime numbers.

(4) Factors of `18` and `35` are `18=2xx3xx3` and `35=5xx7`, as there is no common factor, they too are coprime numbers.

However, in case of (1) factors of `32` and `24` are `32=2xx2xx2xx2xx2` and `24=2xx2xx2xx3`, and common factors are `2xx2xx2=8`. Hence, they are not coprime numbers.

Answer 2

`(1)32,24`

Explanation:

`"a pair of numbers are coprime if they have no "`
`color(blue)"common factors"" other than 1"`

`"compare the factors of each pair of numbers"`

`(1)color(white)(x)32,24`

`"factors of 32 "=1,2,4,8,16,32`

`"factors of 24" =1,2,3,4,6,8`

`32,24" have common factors of "1,2,4,8`

`rArr32,24" are not coprime"`

`(2)color(white)(x)25,32`

`"factors of 25 "=1,5,25`

`"the only common factor between "25" and "32 " is "1`

`rArr25" and " 32" are coprime"`

`"comparing the other pairs confirms that only "`

`32" and "24" are not coprime"`