Here are 10 examples illustrating different methods for quickly dividing numbers:

Example 1: Divide 360 by 6

- Divisibility Rule: 6 is divisible by 2 and 3. Since 360 is also divisible by 2 and 3, you can first divide 360 by 2 (180), and then divide 180 by 3 (60).

Example 2: Divide 672 by 8

- Divide by Multiples: Since 8 is a multiple of 2, first divide 672 by 2 to get 336, then divide 336 by 2 to get 168, and finally divide 168 by 2 to get 84. Therefore, 672 ÷ 8 = 84.

Example 3: Divide 450 by 9

- Divisibility Rule: 9's rule states that the digits' sum must be divisible by 9. In this case, 4 + 5 + 0 = 9, which is divisible by 9. Therefore, 450 ÷ 9 = 50.

Example 4: Divide 128 by 4

- Long Division Shortcut: Start by estimating how many times 4 fits into the first digit of 128, which is 1. Divide 128 by 4 to get 32.

Example 5: Divide 785 by 5

- Mental Approximation: Round 785 to 800 and divide by 5 to get 160 (800 ÷ 5 = 160). Adjust for the rounding to get a close estimate.

Example 6: Divide 117 by 13

- Use Known Facts: If you know that 13 x 9 = 117, then 117 ÷ 13 = 9.

Example 7: Divide 256 by 16

- Divide by Multiples: Since 16 is a power of 2, divide 256 by 2 repeatedly until you reach 1. 256 ÷ 2 = 128, 128 ÷ 2 = 64, and 64 ÷ 2 = 32. Then, 32 ÷ 2 = 16.

Example 8: Divide 583 by 7

- Round and Adjust: Round 583 to 600 and divide by 7 to get around 85. Adjust for the rounding to find a close estimate.

Example 9: Divide 625 by 25

- Divide by Multiples: Since 25 is a square of 5, divide 625 by 5 twice. 625 ÷ 5 = 125, and then 125 ÷ 5 = 25.

Example 10: Divide 910 by 7

- Subtraction Method: Repeatedly subtract 7 from 910 until you can't subtract anymore. You'll subtract 7 around 130 times, so the quotient is around 130.

These examples showcase various techniques to quickly divide numbers using different strategies and methods. Remember that the most suitable method depends on the numbers you're working with and your familiarity with the techniques.