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, 21= 3 × 7, 22= 2 × 11. 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. 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. Explain why successive composted that gives the sequence of GPFs 41,19,79 must all have at least 4 digits and Find the largest composite LESS than 10000 with a GPF of 7, and prove that it is the largest

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, 21= 3 × 7, 22= 2 × 11. 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.

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.

Explain why successive composted that gives the sequence of GPFs 41,19,79 must all have at least 4 digits

and

Find the largest composite LESS than 10000 with a GPF of 7, and prove that it is the largest