But what's a humble number? (2)

Number Theory Level pending

A humble number is a number that consists of prime factors which are less than 10.

How many humble numbers does $100!$ divide?

Infinitely Many

2^{100!-1}

2^{100!} - 1

100!^{2}

100!

0 1 2040850

1 solution

Efren Medallo
Jun 9, 2015

By definition, a humble number is a number whose prime factors consists of 2, 3, 5, or 7. It is a number of the form $2^{a} \times 3^{b} \times 5^{c} \times 7^{d}$ , where $a, b, c$ , and $d$ are non-negative integers.

$100!$ is not a humble number,thus it cannot be a factor of any humble number in existence.

But what's a humble number? (2)

1 solution

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