52 factorial is about 8.0658×10678.0658\times 10^{67}8.0658×1067, which is this exact 68‑digit monster: 80658175170943878571660636856403766975289505440883277824000000000000

What 52! actually means

  • 52! = 52×51×50×⋯×2×152\times 51\times 50\times \dots \times 2\times 152×51×50×⋯×2×1.
  • It has 68 digits and ends with 12 zeros.
  • In card terms, it’s the number of different ways you can order a standard 52‑card deck.

How big is that, intuitively?

Here are some rough comparison points people use to feel the size:

  • 52! ≈ 8.07×10678.07\times 10^{67}8.07×1067.
  • The estimated number of atoms in the observable universe is around 108010^{80}1080, so 52! is “only” a bit smaller, but still in the same cosmic ballpark in terms of digit length.
  • If every different shuffle of a deck was written on its own line in a book, you’d never finish reading even a tiny fraction of them in the lifetime of the universe.

A popular storytelling angle: if every person on Earth shuffled a deck once per second for the entire age of the universe, you’d still almost certainly never see the same exact shuffle twice. This is why people say that any random shuffle you do is overwhelmingly likely to be a configuration that has never existed before.

Mini example with smaller factorials

To see how fast things blow up:

  • 5! = 120
  • 10! = 3,628,800
  • 20! = 2,432,902,008,176,640,000
  • 52! already jumps to that 68‑digit number above.

So “how big is 52 factorial?”
It’s astronomically large—far beyond anything you could ever list, count through, or physically realize in practice.

Information gathered from public forums or data available on the internet and portrayed here.