challenge
11-16-2017, 01:03 AM
Post: #1
 Don Shepherd Senior Member Posts: 745 Joined: Dec 2013
challenge
Without using a CAS or the Internet, how many factors does this number have: 200,560,490,130?
11-16-2017, 01:20 AM
Post: #2
 Paul Dale Senior Member Posts: 1,733 Joined: Dec 2013
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 211 = 2048 in total.

Pauli
11-16-2017, 01:30 AM (This post was last modified: 11-16-2017 01:31 AM by Don Shepherd.)
Post: #3
 Don Shepherd Senior Member Posts: 745 Joined: Dec 2013
RE: challenge
(11-16-2017 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 211 = 2048 in total.

Pauli
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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