For small numbers this operation is easy for large

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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. Discuss UPCAT and other college entrance exam questions and answers at Academic-Clinic’s Facebook Page. We encourage you to answer the questions we post there and actively participate in the discussions on our wall. For UPCAT, ACET, DLSUCET and USTET tips, tricks, news and other college entrance exam information, visit the Academic-Clinic website. Tell your friends and classmates to come find and join us. The more, the merrier. Good luck! AcademicAcademic Aca...
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