3. “The product of three consecutive positive
integers is divisible by 6". Is this statement
true or false? Justify your answer.
TCBSE 2016]
Answers
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).(
6
60
=10).
Taking another set of 3 consecutive integers, say 13, 14, 15
Product of 13, 14, 15 = 13 × 14 × 15 = 2730, which is divisible by six
(\frac {2730}{6}=433).(
6
2730
=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).
Answer:
It is the correct answer.
Step-by-step explanation:
Hope this attachment helps you.
