n-390-is-a-prime-number-less-than-12-and-one-of-the-prime-factor-of-n-is-not-a-prime-factor-of-390-Qty-A-n-Qty-B-3000-

Question Number 178115 by aurpeyz last updated on 12/Oct/22

\frac{n}{390} i s a p r i m e n u m b e r l e s s t h a n 12 a n d

o n e o f t h e p r i m e f a c t o r o f n i s n o t

a p r i m e f a c t o r o f 390 .

Q t y A : n

Q t y B : 3000

Answered by Rasheed.Sindhi last updated on 13/Oct/22

\frac{n}{390} = m (\in P) < 12

n = 390 m

l e t p i s a p r i m e f a c t o r o f n w h i c h i s

n o t a p r i m e f a c t o r o f 390 .

l e t n = p q \land p ∣ m

∵ m \in P ∴ p = m

\frac{n}{390} = p \land p ∣ n b u t p ∤ 390

∴ p \neq 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65,

78, 130, 195, 390

p (< 12) = 7, 11

n = 390 p = 390 \cdot 7, 390 \cdot 11

n = 2730, 4290

Commented by Tawa11 last updated on 13/Oct/22

Great sir

Answered by mr W last updated on 13/Oct/22

\frac{n}{390} = \frac{n}{2 \times 3 \times 5 \times 13} = p

p = 2, 3, 5, 7, 11

\Rightarrow n = 2 \times 3 \times 5 \times 13 \times 7 = 2730 o r

\Rightarrow n = 2 \times 3 \times 5 \times 13 \times 11 = 4290

Commented by Rasheed.Sindhi last updated on 13/Oct/22

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