Homebrew now provides native support for MacBooks with M1 Silicon, installing brew on macOS Big Sur is simple, just open terminal and run the below command,
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)"
You will be prompted to enter password when you run the command and all required tools and packages will be installed.

Installing homebrew M1 Mac
[email protected] / % /bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)"
Password:
==> This script will install:
/opt/homebrew/bin/brew
/opt/homebrew/share/doc/homebrew
/opt/homebrew/share/man/man1/brew.1
/opt/homebrew/share/zsh/site-functions/_brew
/opt/homebrew/etc/bash_completion.d/brew
/opt/homebrew
==> The following new directories will be created:
/opt/homebrew/bin
/opt/homebrew/etc
/opt/homebrew/include
/opt/homebrew/lib
/opt/homebrew/sbin
/opt/homebrew/share
/opt/homebrew/var
/opt/homebrew/opt
/opt/homebrew/share/zsh
/opt/homebrew/share/zsh/site-functions
/opt/homebrew/var/homebrew
/opt/homebrew/var/homebrew/linked
/opt/homebrew/Cellar
/opt/homebrew/Caskroom
/opt/homebrew/Frameworks
==> The Xcode Command Line Tools will be installed.
Press RETURN to continue or any other key to abort
* [new tag] 3.0.0 -> 3.0.0
HEAD is now at 3bcd919a7 Merge pull request #10578
from MikeMcQuaid/formula_bottle_hash
==> Tapping homebrew/core
remote: Enumerating objects: 39, done.
remote: Counting objects: 100% (39/39), done.
remote: Compressing objects: 100% (26/26), done.
remote: Total 906603 (delta 21), reused 26 (delta 13), pack-reused 906564
Receiving objects: 100% (906603/906603), 360.00 MiB | 916.00 KiB/s, done.
Resolving deltas: 100% (617458/617458), done.
From https://github.com/Homebrew/homebrew-core
* [new branch] master -> origin/master
HEAD is now at f1b2a2e9b3 ffmpeg: update 4.3.1_9 bottle.
Warning: /opt/homebrew/bin is not in your PATH.
==> Installation successful!
==> Homebrew has enabled anonymous aggregate formulae and cask analytics.
Read the analytics documentation (and how to opt-out) here:
https://docs.brew.sh/Analytics
No analytics data has been sent yet (or will be during this `install` run).
==> Homebrew is run entirely by unpaid volunteers. Please consider donating:
https://github.com/Homebrew/brew#donations
==> Next steps:
- Add Homebrew to your PATH in /Users/code2care/.zprofile:
echo 'eval $(/opt/homebrew/bin/brew shellenv)' >> /Users/code2care/.zprofile
eval $(/opt/homebrew/bin/brew shellenv)
- Run `brew help` to get started
- Further documentation:
https://docs.brew.sh
Make sure you add the brew installation dir to PATH: Follow this article to do so: https://code2care.org/howto/fix-command-not-found-brew-bash-zsh-on-macos-terminal
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