Division Is Fun

Division is Fun (Tests of divisibility)

For example: 42 6 = 7

Say 42, is exactly divided by 6. It is easy to tell without workout because 6 times 7 is 42, obviously from 6 timetable or 7 time table.

But can you say 732468, is exactly divided by 6 or not without workout?

Yes, we can say. First, we must know what the digit sum of a number is and rules of ending number patterns.

The Digit Sum of a Number

The digit sum of a number, say 134, is just the sum of the digits, 1+3+4=8. If the sum of the digits is greater than nine then the process is repeated.

For example, the sum of the digits for 678 is 6+7+8=21 and the sum of the digits for 21 is 3 so the digit sum of 678 is 3.

Tests of Divisibility

The digit sum and ending digits of a number are vital features in divisibility test of a number.

It is interesting whenever a number is tested for divisibility.

Find the rules of divisibility and examples.

Divisibility Rules

Examples

Is it divisible by 2? Any number ending in 2, 4, 6, 8 or 0 is divisible by 2

Eg: 212, 7394, 856, 1238, 45230

Is it divisible by 5? Any number ending in 5 or 0 is divisible by 5

Eg: 7860, 7935, 125, 1080

Is it divisible by 10? Any number ending in 0 is divisible by 10

Eg: 1230, 100, 370, 9990

Is it divisible by 4? If the last two digits of a number is divisible by 4, then the entire number is divisible by 4.

Eg: 1968, 1996, 2000, 2008, 2012, 2024 and all leap years.

Is it divisible by 9? If digit sum of a number is 9, then the number is divisible by 9.

Eg: 54 (5+4 = 9),

108 (1+0+8 = 9),

729 (7+2+9 =18, 1+8 = 9)

Is it divisible by 3? If digit sum of a number is 3, 6 or 9, then the number is divisible by 3.

Eg: 111 (1+1+1 = 3),

717 (7+1+7 = 15, 1+5 = 6),

9972 (9+9+7+2 = 27, 2+7 = 9)

Is it divisible by 6? If any number is divisible by 3 and 2, then the number is divisible by 6

Eg: 222 (2+2+2 = 3),

780 (7+8+0 = 15, 1+5 = 6),

5274 (5+2+7+4 = 18, 1+8 = 9)

End.