2007-10-01 18:20:47 · 3 answers · asked by albert o 1 in Science & Mathematics ➔ Mathematics
because ABABABs are products of AB and 10101, where 10101 are multiple of 7.
2007-10-01 18:26:10 · answer #1 · answered by Mugen is Strong 7 · 0⤊ 0⤋
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.
2007-10-01 18:28:14 · answer #2 · answered by Northstar 7 · 1⤊ 0⤋
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.
2007-10-02 02:34:56 · answer #3 · answered by kkr 3 · 0⤊ 0⤋