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:

The prime factors of 132 are:
[2, 2, 3, 11]
Learn how we calculated this below

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