# Factoring Integers

Updated 2009-01-22 11:46

## Factorizations of Integers into Prime Numbers

Prime Numbers cannot be factored.
NumberFactorization
1prime
2prime
3prime
42 x 2 = 22
5prime
62 x 3
7prime
82 x 2 x 2 = 23
93 x 3 = 32
102 x 5
11prime
122 x 2 x 3 = 22 x 3
13prime
142 x 7
153 x 5
162 x 2 x 2 x 2 = 24
17prime
182 x 3 x 3 = 2 x 32
19prime
202 x 2 x 5 = 22 x 5

NumberFactorization
Ends in 0Contains 2 x 5
Ends in 5Contains 5
It is evenContains 2
Its last 2 digits are divisible by 4Contains 2 x 2 = 22
Its last 3 digits are divisible by 8Contains 2 x 2 x 2 = 23
Its digits sum to a number divisible by 3Contains 3
Its digits sum to a number divisible by 9Contains 3 x 3 = 32

NumberFactorization
213 x 7
222 x 11
23prime
242 x 2 x 2 x 3 = 23 x 3
255 x 5 = 52
262 x 13
273 x 3 x 3 = 33
282 x 2 x 7 = 22 x 7
29prime
302 x 3 x 5
31prime
322 x 2 x 2 x 2 x 2 = 25
333 x 11
342 x 17
355 x 7
362 x 2 x 3 x 3 = 22 x 32
37prime
382 x 19
393 x 13
402 x 2 x 2 x 5 = 23 x 5

NumberFactorization
41prime
422 x 3 x 7
43prime
442 x 2 x 11 = 22 x 11
453 x 3 x 5 = 32 x 5
462 x 23
47prime
482 x 2 x 2 x 2 x 3 = 24 x 3
497 x 7 = 72
502 x 5 x 5 = 2 x 52
513 x 17
522 x 2 x 13 = 22 x 13
53prime
542 x 3 x 3 x 3 = 2 x 33
555 x 11
562 x 2 x 2 x 7 = 23 x 7
573 x 19
582 x 29
59prime
602 x 2 x 3 x 5 = 22 x 3 x 5

NumberFactorization
61prime
622 x 31
633 x 3 x 7 = 32 x 7
642 x 2 x 2 x 2 x 2 x 2 = 26
655 x 13
662 x 3 x 11
67prime
682 x 2 x 17 = 22 x 17
693 x 23
702 x 5 x 7
71prime
722 x 2 x 2 x 3 x 3 = 23 x 32
73prime
742 x 37
753 x 5 x 5 = 3 x 52
762 x 2 x 19 = 22 x 19
777 x 11
782 x 3 x 13
79prime
802 x 2 x 2 x 2 x 5 = 24 x 5

NumberFactorization
813 x 3 x 3 x 3 = 34
822 x 41
83prime
842 x 2 x 3 x 7 = 22 x 3 x 7
855 x 17
862 x 43
873 x 29
882 x 2 x 2 x 11 = 23 x 11
89prime
902 x 3 x 3 x 5 = 2 x 32 x 5
917 x 13
922 x 2 x 23 = 22 x 23
933 x 31
942 x 47
955 x 19
962 x 2 x 2 x 2 x 2 x 3 = 25 x 3
97prime
982 x 7 x 7 = 2 x 72
993 x 3 x 11 = 32 x 11
1002 x 2 x 5 x 5 = 22 x 52

## References:

http://www.purplemath.com/modules/factnumb.htm
http://mathforum.org/dr.math/faq/faq.divisibility.html