factors

[luckypiscian]

If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

51
54
72
162
50!+2

QA is D considering x as 53*2 = 106
why can't x be 52, i.e. non prime and not a factor of 50!

[jitsy]

x cannot be 52 since 52 is 26*2 and since both both 2 and 26 are present in 50!, 52 is a factor of 50!

[jitsy]

Good question though luckypiscian. Can I ask where this is from. Thank you.

[luckypiscian]

OOPS ... my bad
this is from Veritas

[jitsy]

Haha, np mate, happens!

[vipulgoyal]

the number is 51

1+3+17+51 = 72 ans

[Matt@VeritasPrep]

Hey, I wrote this one! (Though it isn't an original idea )

Vipul, the answer isn't 51, as 51 is a factor of 50! (3 * 17 is part of 50!, so 50! divides by 51.)

[vipulgoyal]

my bad, no is 106, sum of factors are 1+2+53+106 = 162

[jitsy]

Good job Matt! Its a great question!

Hey, I wrote this one! (Though it isn't an original idea )

Vipul, the answer isn't 51, as 51 is a factor of 50! (3 * 17 is part of 50!, so 50! divides by 51.)