Master the 7 pillars of school success

# Prime Factorization

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.

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

5. Write like bases with exponents

​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

## 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