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3. “The product of three consecutive positive integers is divisible by 6". Is this statementtrue or false? Justify your answer.TCBSE 2016] |
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Answer» The statement is true that the PRODUCT of any three consecutive positive numbers can be divisible by 6.Solution:Let take any 3 consecutive integers, say 3,4,5.Product of 3,4,5 = 3 × 4 × 5 = 60, which is divisible by six(\frac {60}{6}=10).( 660 =10).Taking another set of 3 consecutive integers, say 13, 14, 15Product of 13, 14, 15 = 13 × 14 × 15 = 2730, which is divisible by six(\frac {2730}{6}=433).( 62730 =433).Thus, it can be observed that any 3 consecutive numbers CHOSEN randomly has 1 or more even numbers (i.e. divisible by 2) and has 1 or more numbers that is divisible by three . This collectively leads to the product of the three consecutive integers to be divisible by six as (2 × 3 = 6). |
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