Numbers in General Form

The general form of a number is obtained by adding the product of the digits with their place values.

1. The General Form of a Two Digit Number

 \mathrm{ab = a \times 10 + b = 10a + b}

Example

\mathrm{93 = 10 \times 9 + 3}

\mathrm{= 90 + 3}

2. The General Form of a Three Digit Number

\mathrm{abc = 100 \times a + 10 \times b + c = 100a + 10b + c}

Example

\mathrm{256 = 100 \times 2 + 10 \times 5 + 6}

\mathrm{= 200 + 50 + 6}

3. Forming Three-digit Numbers with given three-digits.

If we have a three digit number then we will always get the remainder zero if we rearrange the number in such a way that all the three numbers are different and if we add them all and then divide it by 37. The trick behind it:

Step 1: Let us take any three digit number \mathrm{abc} , which can be written as \mathrm{(100a +10b + c).} .

Step 2: Rearrange the number in such a way that it forms two different numbers. One number can be \mathrm{bca} which can be written as \mathrm{(100b + 10c + a)} and other can be cab which can be written as \mathrm{(100c + 10a + b)} .

Step 3: By adding all the three numbers i.e. \mathrm{abc +bca + cab} cab we get \mathrm{(100a +10b + c) + (100b +10c + a) + (100c + 10a + b) = 111 (a + b + c)}

Step 4: By dividing the number by 37 we will always get the remainder zero.

Example

Try for the number 397.

Solution:

  • Given number is 397.
  • By rearranging we will have two other numbers i.e. 973 and 739.
  • Sum of all the three numbers is 397+ 973 + 739 = 2109.
  • By dividing 2109 by 37 we get 57 i.e. 2109 \mathrm{\div} 37 = 57 and remainder will be zero.
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