# Prime Factorization of 312

## What is the Prime Factorization of 312?

**Answer:**Prime Factors of

**312:**

**2, 2, 2, 3, 13**

or

**2**

^{3}× 3 × 13## Explanation of number 312 Prime Factorization

Prime Factorization of 312 it is expressing 312 as the product of prime factors. In other words it is finding which prime numbers should be multiplied together to make 312.

Since number 312 is a Composite number (not Prime) we can do its Prime Factorization.

To get a list of all Prime Factors of 312, we have to iteratively divide 312 by the smallest prime number possible until the result equals 1.

Here is the complete solution of finding Prime Factors of 312:

The smallest Prime Number which can divide **312** without a remainder is **2**. So the first calculation step would look like:

312 ÷ **2** = 156

Now we repeat this action until the result equals **1**:

156 ÷ **2** = 78

78 ÷ **2** = 39

39 ÷ **3** = 13

13 ÷ **13** = 1

Now we have all the Prime Factors for number 312. It is: **2, 2, 2, 3, 13**

Or you may also write it in exponential form: **2 ^{3} × 3 × 13**

## Prime Factor Tree of 312

We may also express the prime factorization of 312 as a **Factor Tree**:

## Related Calculations

## Prime Factorization Table

Number | Prime Factors |
---|---|

297 | 3^{3} × 11 |

298 | 2, 149 |

299 | 13, 23 |

300 | 2^{2} × 3 × 5^{2} |

301 | 7, 43 |

302 | 2, 151 |

303 | 3, 101 |

304 | 2^{4} × 19 |

305 | 5, 61 |

306 | 2 × 3^{2} × 17 |

307 | 307 |

308 | 2^{2} × 7 × 11 |

309 | 3, 103 |

310 | 2, 5, 31 |

311 | 311 |

312 | 2^{3} × 3 × 13 |

313 | 313 |

314 | 2, 157 |

315 | 3^{2} × 5 × 7 |

316 | 2^{2} × 79 |

317 | 317 |

318 | 2, 3, 53 |

319 | 11, 29 |

320 | 2^{6} × 5 |

321 | 3, 107 |

322 | 2, 7, 23 |

323 | 17, 19 |

324 | 2^{2} × 3^{4} |

325 | 5^{2} × 13 |

326 | 2, 163 |

## About "Prime Factorization" Calculator

**2, 2, 2, 3, 13**). Pick the number for factorization (e.g. '312'). After that hit the 'Calculate' button.

Prime factors are the positive integers having only two factors - 1 and the number itself