What are the solutions to these math problems concerning divisibility, number properties, and basic arithmetic?

$$
100,000,000 - 99,999,999 = 1
$$
The difference is $\boxed{1}$.

3. Given $a=6$ and $b=1$.

$$
42
$$
The value is $\boxed{42}$.

4. a) Seven hundred and forty-five million, two hundred and three thousand, six hundred and twelve is written as $\boxed{745,203,612}$. b) Eighty-nine million, four thousand and seventy is written as $\boxed{89,004,070}$.

5. a) 508,076,314 is written as Five hundred eight million, seventy-six thousand, three hundred fourteen. b) 300,000,009 is written as Three hundred million, nine.

6. a) In 927,534,218, the digit 7 is in the millions place. Its total value is $7 \times 1,000,000 = \boxed{7,000,000}$. b) In 240,815,963, the digit 4 is in the ten millions place. Its total value is $4 \times 10,000,000 = \boxed{40,000,000}$.

7. a) Round 489,736,214 to the nearest hundred million. The hundred millions digit is 4. The digit to its right is 8. Since $8 \ge 5$, we round up the 4. The rounded number is $\boxed{500,000,000}$. b) Round 72,361,983 to the nearest ten million. The ten millions digit is 7. The digit to its right is 2. Since $2 < 5$, we keep the 7 as it is. The rounded number is $\boxed{70,000,000}$.

8. a) The sequence is 2, 6, 18, .... The common ratio is $6 \div 2 = 3$ and $18 \div 6 = 3$. The next three numbers are: $18 \times 3 = 54$ $54 \times 3 = 162$ $162 \times 3 = 486$ The next three numbers are $\boxed{54, 162, 486}$. b) The sequence is 105, 95, 85, .... The common difference is $95 - 105 = -10$ and $85 - 95 = -10$. The next three numbers are: $85 - 10 = 75$ $75 - 10 = 65$ $65 - 10 = 55$ The next three numbers are $\boxed{75, 65, 55}$.

9. The numbers are 308,419,621 and 381,429,216. Comparing the numbers, we look at the digits from left to right. The first digit (hundred millions place) is 3 for both. The second digit (ten millions place) is 0 for the first number and 8 for the second. Since $0 < 8$, the first number is smaller. Arranged in increasing order: $\boxed{308,419,621; 381,429,216}$.

10. a) Test 3456 by 2. A number is divisible by 2 if its last digit is an even number. The last digit of 3456 is 6, which is an even number. Therefore, 3456 is divisible by 2. b) Test 936 by 11. A number is divisible by 11 if the alternating sum of its digits is divisible by 11. For 936: $6 - 3 + 9 = 12$. Since 12 is not divisible by 11, 936 is not divisible by 11.

11. a) Express 84 as a product of prime factors.