Question

In how many ways 540 can be written as a product of two co-prime factors?
(a) 1
(b) 2
(c)3
(d) 4​

Answer 1

$\underline {\pink { co - prime \: numbers : }}$

Numbers which have no common factors other than 1 are called co - prime .

$Given \: number \: 540$

540 = 1 × 540

= 2 × 270

= 3 × 180

= 4 × 135

= 5 × 108

= 6 × 90

= 9 × 60

= 12 × 45

= 15 × 36

= 18 × 30

= 20 × 27

Factors of 540 = { 1,2,2,4,5,6,9,12,15,18,20,27,30,36,45,60,90,108,135,180,270,540 }

$In \: two \: ways \: 540\: can \:be \: written\\as \:a \: product \: of \: two \: co - prime \: factors .\\ i.e .,( 4 \times 135 ) \:and \: ( 5 \times 108)$

Therefore.,

$Option \: \pink { ( b ) } \: correct.$

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