Unformatted text preview: torization. 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 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
 Greatest common factor
Common factor of some numbers  a number, which is a factor of each of them. For example, numbers 36,
60, 42 have common factors 2 and 3 . Among all common factors there is always the greatest one, in our
case this is 6. This number is called a greatest common factor (GCF).
To find a greatest common factor (GCF) of some numbers it is necessary:
1) to express each of the numbers as a product of its prime factors, for example:
360 = 2 · 2 · 2 · 3 · 3 · 5 ,
2) to write powers of all prime factors in the factorization as:
360 = 2 · 2 · 2 · 3 · 3 · 5 = 23 · 32 · 51 ,
Math I 4 Feel free to pass this on to your friends, but please don’t post it online.
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This note was uploaded on 07/21/2013 for the course UPCAT 2014 taught by Professor Otis during the Spring '13 term at University of the Philippines Diliman.
 Spring '13
 OTIS

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