When it comes to claiming Social Security, you get choices. You can file for benefits as early as age 62, or you could postpone your filing until age 70 to maximize your benefits. (Technically, you can claim Social Security past the age of 70, but there's no point, financially speaking, in delaying your filing beyond that point.)

While 62 happens to be the most popular age to sign up for Social Security, some seniors opt to take benefits at 65. But is that the right choice for you?

When Medicare comes into the mix

Age 65 is when Medicare eligibility begins. This doesn't mean you have to enroll in Medicare at 65 on the nose. If you're still working at that point and have access to an employer health insurance plan, you can hold off on registering for Medicare without incurring penalties. But if you don't have access to a health plan through an employer, signing up for Medicare at 65 not only makes sense, but could make it so that Part B, which covers outpatient care, is less expensive throughout your retirement.

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That said, you don't have to sign up for Medicare and Social Security at the same time. And you may not want to.

Your monthly Social Security benefit is calculated based on your 35 highest-paid years in the labor force. And you're entitled to that benefit once you reach full retirement age, or FRA.

FRA doesn't kick in until age 67 for anyone born in 1960 or later. And so while you can file for Social Security at 65, doing so will mean reducing your monthly benefit on a permanent basis.

In fact, if your FRA is 67, signing up at 65 will shrink your benefit by 13.34%. That's a hit you may not want to take, especially if you're entering retirement without much in the way of savings.

Now the one advantage of claiming Social Security at the same time as your Medicare enrollment is getting to have your Part B premiums deducted directly from your benefits. But you can also arrange to have those premiums paid automatically to Medicare from your bank account so you don't have to worry about them -- so that shouldn't be a big driver in your decision.

What's the right move for you?

If you're signing up for Medicare at 65 because you've retired and need health coverage, it could mean that you also need money from Social Security to cover your bills. And so in that case, you may have to sign up in conjunction with Medicare.

But if you run your own business and need health coverage but not money, then it could pay to delay your Social Security claim beyond the age of 65. If you hold out until at least FRA, your benefits won't take a hit, leaving you with less money for life. And if you push yourself to delay your filing past FRA, you might really enjoy a lot more financial flexibility during your senior years.