Linux Mint filesystem full despite home directory being virtually empty. SDA6 file/folder 98% full?

I have Mint installed on an 80GB partition. When I boot up, Mint tells me that "filesystem" is almost full. I typed "df -h" into the the terminal and this is the output:

Filesystem Size Used Avail Use% Mounted on
udev 3.6G 0 3.6G 0% /dev
tmpfs 737M 1.6M 735M 1% /run
/dev/sda6 59G 55G 1.2G 98% /
tmpfs 3.6G 30M 3.6G 1% /dev/shm
tmpfs 5.0M 4.0K 5.0M 1% /run/lock
tmpfs 3.6G 0 3.6G 0% /sys/fs/cgroup
/dev/sda5 511M 24K 511M 1% /boot/efi
tmpfs 737M 36K 737M 1% /run/user/1000
/dev/mmcblk0p1 1.9G 80M 1.8G 5% /media/user/Memory card
/dev/sda2 178G 66G 113G 37% /media/user/

It seems to show that /dev/sda6 is using 55GB of the 80GB partition and that it is 98% full, however I am unsure what sda6 even is. I cannot delete it and it doesn't seem to be a file or folder. What are these sda files, why do they take up so much space and how do I reduce the usage? I simply installed Mint on an 80GB partition and use the home directory to store small files like documents and C code.

EDIT: output of lsblk:

NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sda 8:0 0 238.5G 0 disk
├─sda1 8:1 0 50M 0 part
├─sda2 8:2 0 178G 0 part
├─sda3 8:3 0 499M 0 part
├─sda4 8:4 0 1K 0 part
├─sda5 8:5 0 512M 0 part /boot/efi
└─sda6 8:6 0 59.5G 0 part /run/timeshift/backup
mmcblk0 179:0 0 1.9G 0 disk
└─mmcblk0p1 179:1 0 1.9G 0 part 
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1 Answer

That's not what it shows. df doesn't look for large files or anything like that; it only shows global filesystem statistics, and the first column in df's output shows you the device that each filesystem is stored on.

So /dev/sda6 isn't occupying any space on the partition; rather, it literally is the partition itself. (If you tried to "reduce its size" the partition would become smaller, and you wouldn't gain space, you would actually lose space.)

(Most paths under /dev, such as /dev/sda, represent devices in one way or another. They don't occupy any space themselves; in fact they're not even on your disk – they're all kept in memory; notice that 'df' shows a whole another filesystem mounted on /dev.)

So the important part of df output is:

Filesystem Size Used Avail Use% Mounted on
......... 59G 55G 1.2G 98% /

which means that your / filesystem is 60 GB in size (not 80 GB!), and various files are occupying 55 GB in total. You could use tools like sudo ncdu -x / to find the actual large files.

(Additionally, 5% of the filesystem's total space, i.e. 3.0 GB out of the total 60 GB, is reserved for use by system services in case the filesystem fills up, so it is subtracted from 'Avail'. This percentage can be changed through tune2fs -m.)

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