The hcf of 3x and 105 is 15 find the value of x.

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Solution

Dear student,

$p r i m e f a c t o r i s a t i o n o f 105 = 3 \times 5 \times 7 w r i t i n g 3 x a s 3 x = 3 \times x H C F o f 3 x a n d 105 w i l l b e g i v e n b y t a k i n g a l l t h e c o m m o n t e r m s i n f a c o t r i s t i o n o f b o t h, h e r e 3 i s a c o m m o n f a c t o r o f b o t h, b u t f r o m 5 a n d 7 i n f a c t o r i s a t i o n o f 105, o n l y o n e i s t h w c o m m o n f a c t o r t h a t w i l l g i v e 15 a s H C F, a n d w i l l b e s a m e a s x t h e r e f o r e, H C F, 15 = 3 \times x x = 5,$

Regards

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