MHB Apc.1.1.13 what is the prime factorization of 30,030

[karush]

$\tiny{apc.1.1.13}$
The number 1,001 is the product of the primes 7, 11, and 13
Knowing this,
What is the prime factorization of 30,030?

a, ${3 \cdot 7\cdot 10\cdot 13}$
b. ${30\cdot 7\cdot 11\cdot 13}$
c. ${2 \cdot 5\cdot 7\cdot 11\cdot 13}$
d. ${3\cdot 7\cdot 10\cdot 11\cdot 13}$
e. ${2\cdot 3\cdot 5\cdot 7\cdot 11\cdot 13}$

Ok I never studied number theory so don't know theorems
but a b and d don't have all primes, by observation c won't make it
so that leaves e

I hope

 

[topsquark]

Not bad. I'd say take a look at a couple of factors. It's clearly divisible by 3. It's also clearly divisible by 10 = 2 x 5, so you are left with e).

-Dan

 

[HOI]

You are told that "1001 is the product of the primes 7, 11, and 13" and 30030= 30(1001).
So 30030 is 30(7*11*13) and 30= 3(10)= 2*3*5. 30030= 2*3*5*7*11*13

 

[karush]

ok weird i didn't see that