The U.S. House of Representatives has 435 members because federal law says it does. The Apportionment Act of 1911 set in stone (or, at least, made legal) that number, to first take effect in 1913 (after the Elections of 1912).

That wasn't always the number of representatives in the House. The very first "class" of House members, in 1789, numbered 65. According to Article One, Section 2, Clause 3 of the Constitution:

"Representatives and direct taxes shall be apportioned among the several states which may be included within this union, according to their respective numbers, which shall be determined by adding to the whole number of free persons, including those bound to service for a term of years, and excluding Indians not taxed, three fifths of all other Persons. The actual Enumeration shall be made within three years after the first meeting of the Congress of the United States, and within every subsequent term of ten years, in such manner as they shall by law direct. The number of Representatives shall not exceed one for every thirty thousand, but each state shall have at least one Representative; and until such enumeration shall be made, the state of New Hampshire shall be entitled to chuse three, Massachusetts eight, Rhode Island and Providence Plantations one, Connecticut five, New York six, New Jersey four, Pennsylvania eight, Delaware one, Maryland six, Virginia ten, North Carolina five, South Carolina five, and Georgia three."

That clause contains certain words and phrases–among them "excluding Indians" and "three fifths of all other Persons" which are relevant in other contexts. It is the words pertaining to representation in the House that are relevant here.

As the U.S. grew in population, the number of seats in the House grew. After the 1790 Census, the House representation was set at 105. Ten years later, the number was 142. As more states entered the Union, more representation became available. Further expansion numbers were these:

1810 182 1820 213 1830 240 1840 223 1850 234 1860 241 1870 292 1880 325 1890 356 1900 386

The Apportionment Act of 1911 raised the number to 435. A further law, the Permanent Apportionment Act of 1929, prohibited further increases in the number of House seats. So even as the population of the country grew after that, the number of seats in the House stayed the same. This is why some states gain and lose seats in the House after each Census.

So the number 435 has no special significance. It is just the number that was "on the books" when Congress decided to stop that number growing.

One final note: At the time of the Permanent Apportionment Act, so in 1929, the U.S. had 48 states and 435 members in the House. In 1959, when Alaska and Hawaii joined the Union, membership in the House increased temporarily to 437. The number went back to 435 after the 1960 Census and the 1962 Congressional Elections.

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