verify if the following are composite
1) 357+10
2) 789*1113-514

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Solution

Answer:
We know a composite number has more than two factors

verify : 3 $\times$ 5 $\times$ 7 + 10 is composite
$\Rightarrow$ 3 $\times$ 5 $\times$ 7 + 2 $\times$ 5
$\Rightarrow$ 5 ( 3 $\times$ 1 $\times$ 7 + 2 $\times$ 1 )
$\Rightarrow$ 1 $\times$ 5 $\times$ ( 3 $\times$ 7 + 2 )
Hence 1 , 5 And ( 3 $\times$ 7 + 2 ) are three factors of 3 $\times$ 5 $\times$ 7 + 10 so this is a composite number

Verify 7 $\times$ 8 $\times$ 9 $\times$ 11 $\times$ 13 - 5 $\times$ 14
$\Rightarrow$ 7 $\times$ 8 $\times$ 9 $\times$ 11 $\times$ 13 - 5 $\times$ 2 $\times$ 7
$\Rightarrow$ 7 ( 1 $\times$ 8 $\times$ 9 $\times$ 11 $\times$ 13 - 5 $\times$ 2 $\times$ 1 )
$\Rightarrow$ 1 $\times$ 7 $\times$ ( 8 $\times$ 9 $\times$ 11 $\times$ 13 - 5 $\times$ 2)
Hence 1 , 7 And ( 8 $\times$ 9 $\times$ 11 $\times$ 13 - 5 $\times$ 2) are three factors of 7 $\times$ 8 $\times$ 9 $\times$ 11 $\times$ 13 - 5 $\times$ 14 So this is composite number .

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Similar questions

Q. If

A = {2, 3, 5, 7, 11, 13}

B = {5, 7, 9, 11, 15}

are the subsets of

U = {2, 3, 5, 7, 9, 11, 13, 15}

, verify De Morgan's laws.

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Verify the following

(i) $\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}$

(ii) $\frac{- 5}{8} + \frac{- 9}{13} = \frac{- 9}{13} + \frac{- 5}{8}$

(iii) $3 + \frac{- 7}{12} = \frac{- 7}{12} + 3$

(iv) $\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}$

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

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verify if the following are composite1) 3*5*7+102) 7*8*9*11*13-5*14

verify if the following are composite
1) 357+10
2) 789*1113-514