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Prime Factorization

factor tree 72


1. Draw two branches from your composite numbers (A number divisible by other numbers in addition to itself and one)

2. Continue to draw branches from each composite number.

3. Underline your prime numbers 

4. Create a summary of your underlined prime numbers from least  to greatest.

5. Write like bases with exponents

Prime factorization calculator
Prime Factorization Calculator
​How do you find the prime factorization of a number? Here is a proven technique.
Practice with these numbers and check your work with our Prime factorization calculator

50       475     360     75




2

73

179

283

419

3

79

181

293

421

5

83

191

307

431

7

89

193

311

433

11

97

197

313

439

13

101

199

317

443

17

103

211

331

449

19

107

223

337

457

23

109

227

347

461

29

113

229

349

463

31

127

233

353

467

37

131

239

359

479

41

137

241

367

487

43

139

251

373

491

47

149

257

379

499

53

11

263

383

503

59

157

269

389

509

61

163

271

397

521

67

167

277

401

523

71

173

281

409

541

 

List of Prime Numbers to 500

Prime Factorization Calculator

Common Core Standard: 6.NS.B4

  •  The fundamental theorem of arithmetic states that every positive integer has a single unique prime factorization.  

  • For instance, the prime numbers 2*2*2*11 = 88, which is unique to 88. 

  • Factors can be expressed in powers in order to shorten the prime factorization.  

  • A prime number is any number divisible by itself and one.  
​Prime Factorization is simply finding which prime numbers, when multiplied together, make the original number.
​Prime factorization is finding the factors of a composite number that are all prime. It involves breaking down, or decomposing the number into the prime numbers which when multiplied together equals the original number.

Number 

Prime Factorization 

Number 

Prime Factorization

 1

 Not composite

 51

 3 x 17

 2

 Prime

 52

 2 x 2 x 13

 3

 Prime

 53

 Prime

 4

  2 x 2

 54

 2 x 3 x 3 x 3

 5

 Prime

 55

 5 x 11

 6

 2 x 3

 56

 2 x 2 x 2 x 7

 7

 Prime

 57

 3 x 19

 8

 2 x 2 x 2

 58

 2 x 29

 9

 3 x 3              

 59

 Prime

 10

 2 x 5

 60

 2 x 2 x 3 x 5

 11

 Prime

 61

 Prime

 12

 2 x 2 x 3

 62

 2 x 31

 13

 Prime

 63

 3 x 3 x 7

 14

 2 x 7

 64

 2 x 2 x 2 x 2 x 2 x 2

 15

 3 x 5

 65

 5 x 13

 16

 2 x 2 x 2 x 2

 66

 2 x 3 x 11

 17

Prime

 67

 Prime

 18

 2 x 3 x 3

 68

 2 x 2 x 17

 19

 Prime

 69

 3 x 23

 20

 2 x 2 x 5

 70

 2 x 5 x 7

21

 3 x 7

 71

 Prime

 22

 2 x 11

 72

 2 x 2 x 2 x 3 x 3

 23

 Prime

 73

 Prime

 24

 2 x 2 x 2 x 3

 74

 2 x 37

 25

 5 x 5

 75

 3 x 5 x 5

 26

 2 x 13

 76

 2 x 2 x 19

 27

 3 x 3 x 3

 77

 7 x 11

 28

 2 x 2 x 7

 78

 2 x 3 x 13

 29

 Prime

 79

 Prime

 30

 2 x 3 x 5

 80

 2 x 2 x 2 x 2 x 

 31

 Prime

 81

 3 x 3 x 3 x 3

 32

 2 x 2 x 2 x 2 x 2

 82

 2 x 41

 33

 3 x 11

 83

 Prime

 34

 2 x 17

 84

 2 x 2 x 3 x 7

 35

 5 x 7

 85

 5 x 17

 36

 2 x 2 x 3 x 3

 86

 2 x 43

 37

 Prime

 87

 3 x 29

 38

 2 x 19

 88

 2 x 2 x 2 x 11

 39

 3 x 13

 89

 Prime

 40

 2 x 2 x 2 x 5

 90

 2 x 3 x 3 x 5

41

 Prime

 91

 7 x 13

 42

 2 x 3 x 7

 92

 2 x 2 x 23

 43

 Prime

 93

 3 x 31

 44

 2 x 2 x 11

 94

 2 x 47

 45

 3 x 3 x 5

 95

 5 x 19

 46

 2 x 23

 96

 2 x 2 x 2 x 2 x 2 x 3

 47

 Prime

 97

 Prime

 48

 2 x 2 x 2 x 2 x 3

 98

 2 x 7 x 7

 49

 7 x 7

 99

 3 x 3 x 11

 50

 2 x 5 x 5

 100

 2 x 2 x 5 x 5

 

Prime Factorization Chart up to 100