Factoring into primes

Number Theory Level 2

$\overline{abc}$ is a three digit number, where $a$ is in the hundreds digit, $b$ is in the tens digit and $c$ is in the ones digit.

Let $R(abc)R = (2^a)\times(3^b)\times(5^c)$ ; for example, $R(140)R=( 2^1)\times(3^4)\times(5^0)=162$ .

For how many three digit numbers $\overline{abc}$ does the function $R(abc)R$ yield a prime number?

two one five four three

1 solution

Hana Wehbi
Aug 2, 2017

There are three solutions here $(100),(010),(001)$ . Since we need the three digit number, so there is only one which is $(100)$ and the prime number will be $\boxed{2}$ .

Factoring into primes

1 solution

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