Difference between revisions of "PaC on Divisibility Rules"

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{{delete|Is unnecessary duplicate of [[Divisibility rules]]}}
 
 
=== 2: Last Digit Must Be Even ===
 
=== 2: Last Digit Must Be Even ===
  

Revision as of 17:37, 23 May 2016

2: Last Digit Must Be Even

Let ABCDEF be a 6-digit number. Note the value of "ABCDEF" is:

$100000A + 10000B + 1000C + 100D + 10E + F$

OR $2(50000A + 5000B + 500C + 50D + 5E) + F$

If F is divisible by 2 (i.e. is 2, 4, 6, 8, or 0), then so is the number "ABCDEF"

3: Three Divides The Sum Of The Digits

Let ABCDEF be a 6-digit number. Note the value of "ABCDEF" is:

$100000A + 10000B + 1000C + 100D + 10E + F$

OR $99999A + 9999B + 999C + 99D + 9E + A + B + C + D + E + F$

OR $3(33333A + 3333B + 333C + 33D + 3E) + A + B + C + D + E + F$

If A + B + C + D + E + F is divisible by 3, then so is ABCDEF.

4: Last TWO Digits Must Be Divisible by 4

Let ABCDEF be a 6-digit number. Note the value of "ABCDEF" is:

$100000A + 10000B + 1000C + 100D + 10E + F$

OR $4(25000A + 2500B + 250C + 25D) + 10E + F$

If "EF" is divisible by 4, then so is the number "ABCDEF"

5: Last Digit Must Be 0 or 5

Let ABCDEF be a 6-digit number. Note the value of "ABCDEF" is:

$100000A + 10000B + 1000C + 100D + 10E + F$

OR $5(20000A + 2000B + 200C + 20D + 2E) + F$

If F is divisible by 5 (i.e. is 0 or 5), then so is the number "ABCDEF"

8: Last THREE Digits Must Be Divisible by 8

Let ABCDEF be a 6-digit number. Note the value of "ABCDEF" is:

$100000A + 10000B + 1000C + 100D + 10E + F$

OR $8(12500A + 1250B + 125C) + 100D + 10E + F$

If "DEF" is divisible by 8, then so is the number "ABCDEF"

9: Three Divides The Sum Of The Digits

Let ABCDEF be a 6-digit number. Note the value of "ABCDEF" is:

$100000A + 10000B + 1000C + 100D + 10E + F$

OR $99999A + 9999B + 999C + 99D + 9E + A + B + C + D + E + F$

OR $9(11111A + 1111B + 111C + 11D + E) + A + B + C + D + E + F$

If A + B + C + D + E + F is divisible by 9, then so is ABCDEF.