If 49 A and A49, where A > 0, have a common factor, find all possible values of A.

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Solution

The given numbers are 49A and A49.

A49 is not divisible by 2.

The sum of the digits of each of the numbers 49A and A49 is 13 + A.

Now, for the numbers to be divisible by 3, 13 + A must be divisible by 3.

∴ A = 2, 5 and 8

Now, let A = 7

497 = 7 × 71

749 = 7 × 107

∴ A = 2, 5, 7 and 8

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If 49 A and A49, where A > 0, have a common factor, find all possible values of A.

The given numbers are 49A and A49. A49 is not divisible by 2. The sum of the digits of each of the numbers 49A and A49 is 13 + A. Now, for the numbers to be divisible by 3, 13 + A must be divisible by 3. ∴ A = 2, 5 and 8 Now, let A = 7 497 = 7 × 71 749 = 7 × 107 ∴ A = 2, 5, 7 and 8

The given numbers are 49A and A49.

A49 is not divisible by 2.

The sum of the digits of each of the numbers 49A and A49 is 13 + A.

Now, for the numbers to be divisible by 3, 13 + A must be divisible by 3.

∴ A = 2, 5 and 8

Now, let A = 7

497 = 7 × 71

749 = 7 × 107

∴ A = 2, 5, 7 and 8