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SaniShahbaz

                             Q # 1

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex]
  • 391 = 17×23
  • 391 is not a Prime Number

Explanation:

391

[tex]391\:\mathrm{divides\:by}\:17\quad \:391=23\cdot \:17[/tex]

[tex]=17\cdot \:23[/tex]

17, 23 are all prime number. So no further factorization possible

[tex]=17\cdot \:23[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex]
  • 391 = 17×23
  • 391 is not a Prime Number                      

                          Q # 3

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]
  • 291 = 3×97
  • 291 is not a Prime Number

Explanation:

291

[tex]291\:\mathrm{divides\:by}\:3\quad \:291=97\cdot \:3[/tex]

[tex]=3\cdot \:97[/tex]

3, 97 are all prime number. So no further factorization possible

[tex]=3\cdot \:97[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]
  • 291 = 3×97
  • 291 is not a Prime Number

                           Q # 4

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]
  • 37=37
  • Yes, 37 is a Prime Number  

Explanation:

37

37 is a prime number. So no further factorization possible

[tex]=37[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]
  • 37=37
  • Yes, 37 is a Prime Number                                              

                         

                       Q # 6

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]
  • 411 = 3×137
  • 411 is not a Prime Number

Explanation:

411

[tex]411\:\mathrm{divides\:by}\:3\quad \:411=137\cdot \:3[/tex]

[tex]=3\cdot \:137[/tex]

3, 137 are all prime number. So no further factorization possible

[tex]=3\cdot \:137[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]
  • 411 = 3×137
  • 411 is not a Prime Number

 

                             Q # 7

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]
  • 387 = 3×3×43
  • 387 is not a Prime Number

Explanation:

387

[tex]387\:\mathrm{divides\:by}\:3\quad \:387=129\cdot \:3[/tex]

[tex]=3\cdot \:129[/tex]

[tex]129\:\mathrm{divides\:by}\:3\quad \:129=43\cdot \:3\\=3\cdot \:3\cdot \:43[/tex]

3, 43 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:43[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]
  • 387 = 3×3×43
  • 387 is not a Prime Number                    

                      Q # 9

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]
  • 113 = 113
  • Yes, 113 is a Prime Number

Explanation:

113

113 is a prime number. So no further factorization possible

[tex]=113[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]
  • 113 = 113
  • Yes, 113 is a Prime Number                          

                    Q # 16

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]
  • 293 = 293
  • Yes, 293 is a Prime Number

Explanation:

293

[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]

[tex]=293[/tex]

[tex]293\mathrm{\:is\:a\:prime\:number,\:therefore\:no\:factorization\:is\:possible}[/tex]

[tex]=293[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]
  • 293 = 293
  • Yes, 293 is a Prime Number

                            Q # 17

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]
  • 451=11×41
  • 451 is not a Prime Number

Explanation:

451

[tex]451\:\mathrm{divides\:by}\:11\quad \:451=41\cdot \:11[/tex]

[tex]=11\cdot \:41[/tex]

11, 41 are all prime number. So no further factorization possible

[tex]=11\cdot \:41[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]
  • 451=11×41
  • 451 is not a Prime Number

                      Q # 18

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]
  • 459 = 3×3×3×17
  • 459 is not a Prime Number

Explanation:

459

[tex]459\:\mathrm{divides\:by}\:3\quad \:459=153\cdot \:3[/tex]

[tex]=3\cdot \:153[/tex]

[tex]153\:\mathrm{divides\:by}\:3\quad \:153=51\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:51[/tex]

[tex]51\:\mathrm{divides\:by}\:3\quad \:51=17\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

3, 17 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]
  • 459 = 3×3×3×17
  • 459 is not a Prime Number

                      Q # 19

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]
  • 385 = 5×7×11
  • 385 is not a Prime Number

Explanation:

385

[tex]385\:\mathrm{divides\:by}\:5\quad \:385=77\cdot \:5[/tex]

[tex]=5\cdot \:77[/tex]

[tex]77\:\mathrm{divides\:by}\:7\quad \:77=11\cdot \:7[/tex]

[tex]=5\cdot \:7\cdot \:11[/tex]

5, 7, 11 are all prime number. So no further factorization possible

[tex]=5\cdot \:7\cdot \:11[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]
  • 385 = 5×7×11
  • 385 is not a Prime Number

                   Q # 20

Answer:

  • [tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]
  • 162 = 2×3×3×3×3
  • 162 is not a Prime Number

Explanation:

162

[tex]162\:\mathrm{divides\:by}\:2\quad \:162=81\cdot \:2[/tex]

[tex]=2\cdot \:81[/tex]

[tex]81\:\mathrm{divides\:by}\:3\quad \:81=27\cdot \:3[/tex]

[tex]=2\cdot \:3\cdot \:27[/tex]

[tex]27\:\mathrm{divides\:by}\:3\quad \:27=9\cdot \:3[/tex]

[tex]=2\cdot \:3\cdot \:3\cdot \:9[/tex]

[tex]9\:\mathrm{divides\:by}\:3\quad \:9=3\cdot \:3[/tex]

[tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex]

[tex]2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex]

So,

  • [tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]
  • 162 = 2×3×3×3×3
  • 162 is not a Prime Number

Keywords: prime factor

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