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No. Goodbacklinks are one of the most important factors, as they are a source of traffic to the site, and a souce for Google to validate your site's content. if you have a ton of good links, but the rest of the site is garbage, you probably wont get very good results. The algorithm looks at over 200 separate bits of information when determining where to rank a site. Are backlinks high on that list? Absolutely. Does that mean that you can have thin content, bad optimization and design? No. Stating that "Backlinks are the most important factor in SEO" sounds more like a marketing phrase used by that company to sell their services.