Becoming a homeowner requires a lot of cash, but a college degree can sometimes make it harder.

In 30 of the top 100 markets in the country, saving for a 20% down payment is faster without a college degree, according to a new study from Trulia.

"In those markets, a household with a college degree isn't making that much more than a household without," said Ralph McLaughlin, Trulia's housing economist. "The burden that student debt brings to a household with a college degree makes it slower to save for a down payment."

A home is the biggest purchase most people will make, and there's been a lack of buying activity among Millennials. Student loan debt tends to get blamed. While going to college usually means higher lifetime earnings, hefty student loans can erode savings and make it harder to accumulate a down payment.

"It's pretty clear cut that most new home buyers feel that saving up for a down payment is their biggest obstacle to buying a first home," said McLaughlin.

Millennials without a degree can save for a down payment at least one year faster than college grads in Columbia, S.C., El Paso, Texas, Las Vegas and Daytona Beach, Fla.

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But one state is a big exception.

The California market is particularly tough to become a homeowner. Seven out of the 10 housing markets where it takes the longest to save for a down payment are located in The Golden State.

But those with a degree have an advantage there. Not only is the income premium for a college degree high in the state, homes are very expensive and prices continue to rise, according to McLaughlin. "Only those with the highest income and high-income growth trajectories can save for a down payment."

In San Francisco -- which is experiencing double-digit price gains -- it will take 25-30-year-olds with a college degree nearly 30 years to save for a 20% down payment on a median-priced home. And for those without a diploma in that age group, it's nearly impossible to save the cash to put down.

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Outside of California's heated housing market, there are many markets where saving for a down payment takes less than seven years for a young person, with or without a degree. Buyers in Detroit face the smallest wait time at 4.1 years with a college degree and 5.3 without.

Ohio is also an affordable options for Millennial buyers.

"Ohio is a state that if you want to buy a house, it's going to be your best shot at doing so," said McLaughlin. "You are going to be able to do it faster than any other state in the country -- every major Ohio market makes the list."

Here are the housing markets where Millennials can save for a 20% down payment the fastest, according to Trulia:

With a college degree:

Detroit: 4.1 years
Camden, NJ: 5.3 years
Dayton, OH: 5.7 years
Akron, OH: 5.9 years
Cleveland, OH: 6.1 years
Buffalo, NY: 6.3 years
Rochester, NY: 6.3 years
Toledo, OH: 6.6 years
Pittsburgh: 6.7 years
Kansas City, MO: 6.8 years

Without a college degree:

Detroit: 5.3 years
Dayton, OH: 5.3 years
Buffalo, NY: 5.4 years
Akron, OH: 5.7 years
Toledo, OH: 5.8 years
Camden, NJ: 5.9 years
Cleveland, OH: 5.9 years
Rochester, NY: 6.3 years
Pittsburgh, PA: 6.3 years
Syracuse, NY: 6.4 years

Trulia projected the 20-year earnings potential for those currently aged 25-30 with and without a college degree and projected home price growth rate for the 100 largest metro areas in the U.S. The calculations also took into account 10% of income going toward student loan payments.