2026-04-19

Problem — 2026-04-19

Easy

Easyprobability

You randomly pick a number from $\{1, 2, \ldots, 100\}$ . What is the probability that it is relatively prime to $100$ ?

Express as a fraction

Show solution

We need

\phi(100)/100

where

\phi

is Euler's totient function. Since

100 = 2^2 \cdot 5^2

, we have

\phi(100) = 100 \cdot (1 - 1/2)(1 - 1/5) = 100 \cdot \frac{1}{2} \cdot \frac{4}{5} = 40

. The probability is

\frac{40}{100} = \frac{2}{5}