# Prime Factors Calculator

Find the prime factors for a number, including large numbers. The calculator will also indicate if the number is a prime number or not.

The *prime factors* of a number are a set of prime numbers, that when multiplied together equal the number.

A *prime number* is a number that is only divisible by itself and 1.

Also see our factors calculator to find all factors for a number, including the greatest common factor.

## Solution

## How Do You Find the Prime Factors of a Number

*Prime factorization* of a number is the act of finding all of the prime factors of a number. This can be done by continuing to divide the number into smaller numbers, and dividing those numbers into smaller numbers again until none of the numbers can be further reduced. The factorization tree above shows how this is done.

To find the prime factors of the number 132, start by dividing 132 by 2, which equals 66. 2 is a prime number and cannot be divided, but 66 can be divided into 33 and 2. 33 can also be divided again into 11 and 3. The prime factors of 132 are thus [11,3,2,2], which are the prime numbers that can be multiplied together to get 132.

Using the tree pattern, prime factors can be found by first dividing each factor by each of the prime numbers until each factor is a prime number. Start by dividing the number by 2, if it cannot be evenly divided then try to divide by 3, then 5, and so on. See our list of all of the prime numbers under 1000 below, which is a helpful reference to see what prime numbers to use to divide factors by.

## List of Prime Factors Under 1000

2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 |

31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 |

73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 |

127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 |

179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 |

233 | 239 | 241 | 251 | 257 | 263 | 269 | 271 | 277 | 281 |

283 | 293 | 307 | 311 | 313 | 317 | 331 | 337 | 347 | 349 |

353 | 359 | 367 | 373 | 379 | 383 | 389 | 397 | 401 | 409 |

419 | 421 | 431 | 433 | 439 | 443 | 449 | 457 | 461 | 463 |

467 | 479 | 487 | 491 | 499 | 503 | 509 | 521 | 523 | 541 |

547 | 557 | 563 | 569 | 571 | 577 | 587 | 593 | 599 | 601 |

607 | 613 | 617 | 619 | 631 | 641 | 643 | 647 | 653 | 659 |

661 | 673 | 677 | 683 | 691 | 701 | 709 | 719 | 727 | 733 |

739 | 743 | 751 | 757 | 761 | 769 | 773 | 787 | 797 | 809 |

811 | 821 | 823 | 827 | 829 | 839 | 853 | 857 | 859 | 863 |

877 | 881 | 883 | 887 | 907 | 911 | 919 | 929 | 937 | 941 |

947 | 953 | 967 | 971 | 977 | 983 | 991 | 997 |

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