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Factorization. Resolution into prime factors

Any composite number can be presented as a product of prime factors by the single way. For example,

48 = 2 · 2 · 2 · 2 · 3, 225 = 3 · 3 · 5 · 5, 1050 = 2 · 3 · 5 · 5 · 7.

For small numbers this operation is easy. For large numbers it is possible to use the following way. Consider the number 1463. Look over prime numbers one after another from the table:

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

and stop, if the number is a factor of 1463. According to the divisibility criteria, we see that numbers 2, 3 and 5 aren’t factors of 1463. But this number is divisible by 7, really, 1463 : 7 = 209. By the same way we test the number 209 and find its factor: 209 : 11 = 19. The last number is a prime one, so the found prime factors of 1463 are: 7, 11 and 19, i.e. 1463 = 7 · 11 · 19. It is possible to write this process using the following record:

Number	Factor
1463	7
209	11
19	19

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