Which of the options below gives a pair of co-prime numbers?

Correct option is C

Given:

Pair of numbers (196 , 343),(228 , 247),(161 , 192) and (156 , 234)

Formula Used:

Co-prime numbers are number which have one as their common factor or their HCF is 1

Solution:

Checking for common factors:

a) (196,343)

196 = $$2^2 \times 7^2$$​​

343 $$=7^3$$​​

Both have a common factor $$7^2$$​or HCF 49

Hence the pair(196,343) is not a co-prime number

b) (247,228)

247 =$$13 \times 19$$​​

228 =$$2^3 \times 3 \times 19$$​​

Their HCF is 19

Hence the pair(247,228) is not a co-prime numbers

c) (161,192)

161 = $$7 \times 23$$​​

192 =$$2^6 \times 3$$​​

HCF = 1 

Hence (161,192) have no other factor other than 1 hence 161 and 192 are co-prime numbers

d) (156,234)

156 = $$2^2 \times 3 \times 13$$​​

234$$=2 \times 3^2 \times 13$$​​

HCF (156,234) $$= 2\times 3 \times 13 = 78$$​​

Hence (156,234) are not co-prime numbers