35% is payment history. Any late payment at any point will hurt you but the further in the past it is the less it affects you. Think of it like, "unblemished" is better than "pretty good" and a creditor wants to see how you've paid everyone else back before giving you access to thousands of dollars.
30% is amount owed. Your credit limits report, as do the amounts you owe. Keeping this ratio below 10% is what is ideal. And this does go across all open accounts. Which is why often a score will drop after an installment loan has been paid off.
15% is length of credit history. They are looking to see that you are good at keeping your accounts long term. It's an average of all open accounts on your report.
10% is new credit. Don't keep looking around for new credit. Keep hard pull inquiries down and honor what you have and this will stay up.
10% is credit mix. Don't put all your eggs in one basket, you need to mix up revolving accounts (credit cards) with installment accounts (car, mortgage, etc).
To answer the question, the lenders want you to have your accounts open as long as possible (loyalty), and some degree of certainty that they will be paid back based on your entire payment reputation.
