1.

If a perfect square, not divisible by 6, be divided by 6, the remainder will be1). 1, 3 or 52). 1, 2 or 53). 1, 3 or 44). 1, 2 or 4

Answer»

Any number can be expressed in the form (6k + n), where k is an integer, and n varies from 0 to 5.

Now, when the square of this number is divided by 6, the REMAINDER will be the same as the remainder obtained by dividing n2 by 6.

For square of (6k + 1), remainder will be the same as remainder obtained by dividing 12 by 6, i.e. 1.

For square of (6k + 2), remainder will be the same as remainder obtained by dividing 22 by 6, i.e. 4.

For square of (6k + 3), remainder will be the same as remainder obtained by dividing 32 by 6, i.e. 3.

For square of (6k + 4), remainder will be the same as remainder obtained by dividing 42 by 6, i.e. 4.

For square of (6k + 5), remainder will be the same as remainder obtained by dividing 52 by 6, i.e. 1.

Clearly, the remainder is 1, 3 or 4.


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