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why all numbers of the form ABABAB are divisible by 7?
2 Answers
- Anonymous1 decade agoFavorite Answer
Because ABABAB = AB*10101
10101 is divisible by 7.
- 1 decade ago
When we relate equal digit-numbers either as a 2D square matrix or as a 3D cube matrix a specific diagonal positions are of the form ABAB (2D)or ABABAB(3D)
In 2D, it is 0000,0101, 0202...so on. (In other words all said numbers (except 0000) are divisible by 0101.
In 3D, it is 000000, 010101, 020202...so on. (In other words all said numbers (except 000000) are divisible by 010101.
Fact is that all 2Dmatrix -diagonal numbers are divisible by 0101. (It also applies to endless similar 2D numbers)
Similarly. all 3D-diagonal numbers are divisible by "010101". (It also applies to endless similar 3D numbers).
It is a sound number application principle!
As regards to your question 010101 is 7*1443 which is reason for said divisibility of all numbers of the form ABABAB! Basically it is a 3D number form!
Regards.
