Americans' personal incomes grew hardly at all in April as wages and salaries, showing the impact of rising unemployment and shorter work weeks, fell at an annual rate of $7.6 billion, the Commerce Department reported yesterday.

Reflecting the full onset of the recession, consumers meanwhile cut back their purchases of durable goods for the third month in a row, the department also said. Purchases of automobiles, appliances and similar items were 12 percent lower in April than in January.

The consumer spending cuts have been so large that Americans are saving more even though their incomes are rising much more slowly than they were only a few months ago.

The savings rate -- personal saving as a percentage of disposable personal income -- hit a low of 3.4 percent in December and January compared with a more normal level of between 5 percent and 6 percent. By last month it had climbed back to 4.2 percent. Each percentage point represents about $17.5 billion worth of income that could be saved or spent.

Commerce said increases in interest income, transfer payments and other non-wage income slightly more than offset the $7.6 billion drop in wages and salaries as well as a $2.2 billion drop in farm proprietors' income.

Altogether, personal income was running at a $2.070 trillion annual rate in April, up $500 million from March. It was the smallest increase since July 1975.

Meanwhile, the Federal Reserve reported that the nation's factories operated at only 81 percent of capacity last month, the lowest rate since February 1977.

Automobile assembly plants were operating about 40 percent below their level of output late in 1978, the Fed said. Output at factories making rubber, metals, plastics and construction products was off about 10 percent from levels a year earlier.

Meanwhile, the downward spiral of the banking industry's prime lending rate continued. Morgan Guaranty Trust Co. of New York lowered its prime rate half a point to 16 percent.

Morgan Guaranty, the nation's fifth largest bank, was the first major bank to lower its rate to 16 1/2 percent last week, a rate that has become general among major banks.

Personal outlays for durable goods, nondurables and services fell $3 billion last month, Commerce said. Spending for nondurables such as food, gasoline and clothing rose by only $1.2 billion to $656 billion, but undoubtedly declined after adjustment for inflation. Outlays for services climbed by $7.4 billion to $772.7 billion.

The very sharp drop in burying of consumer durables from an annual rate of $213.1 billion in March to $201.4 billion last month pulled down the total. By far the biggest drop has been in automobile purchases, the reason for such a low operating rate at auto plants.

The implicit price deflator for personal consumption expenditures, which some economists regard as a better measure of inflation actually experienced by consumers, rose 10.9 percent in the 12 months ended in March, the department said.

Over the same 12 months, the consumer price index rose 14.7 percent. The CPI has risen faster for the last two or three years because it treats housing costs differently.