# Prime Factors Calculator

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

## Solution:

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

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.

*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.

Using the tree pattern, prime factors can be found by first dividing the number by each of the prime numbers until a prime number can be divided evenly. Start by dividing the number by 2, if it cannot be evenly divided then try to divide by 3, then 5, and so on. The prime number that was used is a prime factor and the other number is a factor.

See the 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.

Now, divide the factor by each prime number until it can be divided evenly, resulting in another prime factor and another factor.

Continue dividing each factor by each of the prime numbers until each factor is a prime number.

You might also find our factors calculator helpful to find all factors for a number.

**For example,** let’s 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 so it is a prime factor.

However, 66 can be divided by 2 again to get 33. We already know that 2 is a prime factor.

We can divide 33 by 3 to get 11. 3 is a prime number so it’s also a prime factor. 11 cannot be divided again and so it is also a prime factor.

Thus, the prime factors of 132 are **[11,3,2,2]**. These are all prime numbers, and if we multiply them all together we’ll get 132.

## List of Prime Factors Under 1,000

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 |