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]

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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.

Tree demonstrating how to find the prime factors for a number by continuing to divide the number into smaller parts — Illustration demonstrating the factorization 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

This table contains all of the prime numbers under 1,000, in order from smallest to largest.
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

Solution:

On this page:

How Do You Find the Prime Factors of a Number

List of Prime Factors Under 1,000

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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

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

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