Question

Which of the following numbers are co-prime?
a) $18$ and $35$
b) $15$ and $37$
c) $30$ and $415$
d) $17$ and $68$
e) $216$ and $215$
f) $81$ and $16$

• A. a,b and f
• B. a,b,e and f
• C. ab,c and f
• D. b,d and f

Answer 1

Answer: (B)

a,b,e and f

Two numbers are co-prime, if the only positive integer that divides both of them is $1$. That is, their H.C.F. $=1$

(a)

$18=1\times 2\times 3\times 3$

$35=1\times 5\times 7$

$H.C.F.=1$

So, the numbers are co-prime.

(b)

$15=1\times 3\times 5$

$37=1\times 37$

$H.C.F.=1$

So, the numbers are co-prime.

(c)

$30=1\times 2\times 3\times 5$

$415=1\times 5\times 83$

$H.C.F.=5$

So, the numbers are not co-prime.

(d)

$17=1\times 17$

$68=1\times 2\times 2\times 17$

$H.C.F.=17$

So, the numbers are not co-prime.

(e)

$216=1\times 2\times 2\times 2\times 3\times 3\times 3$

$215=1\times 5\times 43$

$H.C.F.=1$

So, the numbers are co-prime.

(f)

$16=1\times 2\times 2\times 2\times 2$

$81=1\times 3\times 3\times 3\times 3$

$H.C.F.=1$

So, the numbers are co-prime.