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The number (516 – 416) is exactly divisible by three three digit numbers. The smallest of these numbers is ?
1. 153
2. 163
3. 173
4. 183
5. None

1 Answer

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Correct Answer - Option 1 : 153

Calculation:

⇒ (516 – 416) = (58 – 48) × (58 + 48)

⇒ (54 – 44) (54 + 44) (58 + 48)

⇒ (52 – 42) (52 + 42) (54 + 44) (58 + 48)

⇒ 9 × 41 × 881 × (58 + 48)

⇒ 9 × 41 × 881 × 456161

⇒ 9 × 41 × 881 × 17 × 26833

⇒ 26833 is a prime number.

⇒ The smallest three digit number which is a factor of the given number is 17 × 9 = 153

∴ The required result will be 153.

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