Question

The H.C F of two numbers is 43 and their
sum is 430. Total number of distinct pairs of
two such numbers is​

Answer 1

ANSWER

43 is a prime number having factors 1 and 43

since there sum is 430

let these are x and y

x+y = 430

43 × a + 43 × b = 430

where a and b are coprime numbers having fators 1 and itself

43 (a+b) = 430

a+b = 10

we have to find pair a and b such that a and b are co prime and a+b=10

=> b = 10-b

if a = 1 b= 9 wrong b is not co prime here

similarly on checking all

we get

( 7,3)

(5,5)

(3,7)

so total pair 3

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