Question

Find the prime no of factors of (6)^10* (17)^17*(19)^27

Answer 1

Hi ,

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We know that ,

C = x^a × y^b × z^c× ...

Where x , y , z are prime ,

then

Number of factors = ( a + 1 )(b+1)(c+1)..

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Now ,

( 6 )^10 × ( 17 )^17 × ( 19 )^27

= ( 2 × 3 )^10 × ( 17 )^17 × ( 19 )^27

= ( 2 )^10 × ( 3 )^10 × ( 17 )^17 × ( 19 )^27

Number of factors = ( 10 + 1 ) ( 10 + 1 ) ( 17 + 1 ) ( 27 + 1 )

= 11 × 11 × 18 × 28

I hope this helps you.

: )