challenge

[Don Shepherd]

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

[Paul Dale]

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

[Don Shepherd]

(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