why all numbers of the form ABABAB are divisible by 7?

Mugen is Strong2007-10-01T22:26:10Z

Favorite Answer

because ABABABs are products of AB and 10101, where 10101 are multiple of 7.

00

Northstar2007-10-01T22:28:14Z

Split the number into two pieces and check to see if they are divisible by 7.

ABABAB = (10000B + 100B + B) + (100000A + 1000A + 10A)

ABABAB = 10101B + 101010A

But 10101 / 7 = 1443

So we have:

10101B + 101010A = 1443B + 14430A which is an integer

So all numbers of the form ABABAB are evenly divisible by 7.

10

kkr2007-10-02T06:34:56Z

An example of 'number form' stated by you is...

131313, which is technically 13*(010101)

All numbers like this has said common factor '010101'

As 10101/7 is 7* 1443, said 7 is a factor of all numbers of the form ABABAB!

Regards.

00

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