Data Centric Approach For 404 Optimization

To find the 404 error pages for few pages it is not hard but it is very critical when it comes to find out thousands of 404 pages.
To sort out this problem there are two metrics, to have a glance over back-links which are the quality links to your site and landing page visits of your site in analytics.

Pull Landing Page Data

Prefer to check the landing pages in analytics Content > Site Content > Landing Pages.

Get Your Backlinks Data

Check the back links to your site using avail of different tools like
Open Site Explorer
Majestic
Ahrefs
Google Webmaster Tools (Traffic > Links to Your Site > Your Most Linked Content > More)
There are two metrics to find out huge number of 404 pages. They are:
Screaming Frog
GWT(Google Webmaster Tool)

1. By using Screaming Frog:

With the use of Screaming frog, find out 404 errors after running a scan of the site, go to Response codes > filter:client error(4XX) > export.

2. By using Google Webmaster Tools (GWT):

To remove 404 pages with Google webmaster tools, go to health > crawl errors > URL errors > Web or Mobile : Not found > Download

Remove downloads related to csv except the list of 404 URLs and save the file as an xlsx file.

By this data-centric approach, you can easily identify the address of back links and you can easily fix it.