DIVISIBILITY RULE FOR 7
MULTIPLY 124 124 124 ...CYCLICALLY(RECURRING)WITH THE DIGITS OF THE GIVEN NATURAL NUMBER FROM LEFT TO RIGHT. IF THE DIFFERNCE OF THE NUMBERS OBTAINED ON ADDING THE ALTERNATE VALUES SO FORMED BY THE ABOVE SAID OPERATIONS (MULTIPLICATION)SEPERATELY IS DIVISIBLE BY 7 THEN THE GIVEN NATURAL NUMBERIS DIVISIBLE BY 7
FOR Eg:
4 0 8 8(ANY GIVEN NUMBER)
1 2 4 1
(*) 4 0 8 8
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4 0 32 8
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ADDITION OF THE ALTERNATE VALUES 4 + 32 = 36,
AND 0 + 8 = 8
NOW ITS DIFFERENCE IS 36 - 8 = 28.
SINCE '28' IS DIVISIBLE BY '7' THE GIVEN NATURAL NUMBER IS DIVISIBLE BY '7' OR IF THIS PROCESS IS CONTINUED FURTHER WE ULTIMATELY ARRIVE AT EITHER '0' OR '7' AND ARE CLEARLY DIVISIBLE BY '7'.
MORE, SIMPLY FIRST REDUCE EACH DIGIT OF THE GIVEN NATURAL NUMBER BY SUBTRACTING '7' IF BIGGER THAN OR EQUAL TO '7' THEN APPLY THE ABOVE SAID TOOL
Eg:
4 0 8 8
(-) 7 7
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4 0 1 1
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NOW DIVISIBILTY FOR 7
1 2 4 1
(*)4 0 1 1
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4 0 4 1
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ADDITION OF ALTERNATE VALUES 4 + 4 = 8
AND 0 + 1 = 1
NOW ITS DIFFERENCE IS 8 - 1 = 7 IS CLEARLY DIVISIBLE BY '7' SO IS THE GIVEN NATURAL NUMBER.
THIS TOOL CAN BE APPLIED FOR ANY NATURAL NUMBER HOW EVER BIG OR SMALL MAY BE.
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