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

The prime factors of 132 are [2, 2, 3, 11]


How Do You Find the Prime Factors of a Number

Find the prime factors for a number by continuing to divide the number into smaller parts

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