challenge

11162017, 01:03 AM
Post: #1




challenge
Without using a CAS or the Internet, how many factors does this number have: 200,560,490,130?


11162017, 01:20 AM
Post: #2




RE: challenge
Prime factorisation by hand didn't take long and it revealed 11 factors. Each can be present or absent for each factor so 2^{11} = 2048 in total.
Pauli 

11162017, 01:30 AM
(This post was last modified: 11162017 01:31 AM by Don Shepherd.)
Post: #3




RE: challenge
(11162017 01:20 AM)Paul Dale Wrote: Prime factorisation by hand didn't take long and it revealed 11 factors. Each can be present or absent for each factor so 2^{11} = 2048 in total.Congratulations Pauli! 200,560,490,130 is the product of the first 11 prime numbers. To find the total number of factors of a number, determine the numbers prime factors, then add 1 to each exponent and then multiply those numbers together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2,048 

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