11 GPFs Positive integers (counting numbers) which have more than two factors are called composite numbers or simply composites. They are not prime but they do have factors which are prime. For example, here are some prime factorisations: 20 = 2 × 2 × 5, Thus the greatest prime factors (GPFs) of 20, 21, 22 are 5, 7, 11 respec- 21 = 3 × 7, 22 = 2 x 11. tively. The list of GPFs of successive composites is called a GPF sequence. For example, the sequence of GPFs for the composites from 40 to 49 is 5, 7, 11, 5, 23, 3, 7. Note that 41, 43, and 47 are prime and do not contribute to the sequence of GPFs. atorget a Find the sequence of GPFs for the composites from 60 to 65. b Explain why successive composites that give the sequence of GPFs 41, 19, 79 must all have at least four digits. c Find the smallest successive composites that give the sequence of GPFs 17, 73, 2, 19. 510, 511,512, 513 d Find the largest composite less than 10 000 with a GPF of 7 and prove that it is the largest. 7, 19, 23, 29, 31, 37,
11 GPFs Positive integers (counting numbers) which have more than two factors are called composite numbers or simply composites. They are not prime but they do have factors which are prime. For example, here are some prime factorisations: 20 = 2 × 2 × 5, Thus the greatest prime factors (GPFs) of 20, 21, 22 are 5, 7, 11 respec- 21 = 3 × 7, 22 = 2 x 11. tively. The list of GPFs of successive composites is called a GPF sequence. For example, the sequence of GPFs for the composites from 40 to 49 is 5, 7, 11, 5, 23, 3, 7. Note that 41, 43, and 47 are prime and do not contribute to the sequence of GPFs. atorget a Find the sequence of GPFs for the composites from 60 to 65. b Explain why successive composites that give the sequence of GPFs 41, 19, 79 must all have at least four digits. c Find the smallest successive composites that give the sequence of GPFs 17, 73, 2, 19. 510, 511,512, 513 d Find the largest composite less than 10 000 with a GPF of 7 and prove that it is the largest. 7, 19, 23, 29, 31, 37,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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please only answer parts b and d, as i have already answered parts a and c
Transcribed Image Text:11 GPFs
Positive integers (counting numbers) which have more than two factors
are called composite numbers or simply composites. They are not prime
but they do have factors which are prime. For example, here are some
prime factorisations: 20= 2 × 2 × 5,
Thus the greatest prime factors (GPFs) of 20, 21, 22 are 5, 7, 11 respec-
21 = 3 × 7,
22 = 2 × 11.
tively.
The list of GPFs of successive composites is called a GPF sequence.
PELO ovqU
For example, the sequence of GPFs for the composites from 40 to 49 is
5, 7, 11, 5, 23, 3, 7. Note that 41, 43, and 47 are prime and do not
contribute to the sequence of GPFs.
aurorgon
a Find the sequence of GPFs for the composites from 60 to 65.
b Explain why successive composites that give the sequence of GPFs
41, 19, 79 must all have at least four digits.
c Find the smallest successive composites that give the sequence of
GPFs 17, 73, 2, 19.
510, 511,512, 513
d Find the largest composite less than 10 000 with a GPF of 7 and prove
that it is the largest.
23,5,7,11, 13, 17, 19, 23, 29, 31, 37,
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