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The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

Grade:12

3 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

(i) 2 × 3 × 4 = 24 which is divisible by 6
(ii) 5 × 6 × 7 = 210 which is divisible by 6
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Thanks
Ram Kushwah
110 Points
3 years ago
Let the consecutive numbers are
Case I: first number is odd
3 x 4 x 5 =60
60 =6 x10 ,so 60 is divisible by 6
*******************************************
Case II: first number is even
2 x 3 x 4=24
here 24=6x 4 
so 24 is divisible by 6
 
Thus
The product of three consecutive number is divisible by 6
Shraddha Singh
273 Points
2 years ago
Dear Student,
 
Let the three consecutive numbers be x , x+1, x+2
 
Their product will be x(x+1)(x+2) = x(x² + 3x + 2) = x³ + 3x² + 2x 
 
Putting value of x as 1 = 1+3+2 = 6
Value as 2 = 8+12+4 = 24 ,i.e., divisible by 6
 
Hence, the product of three consecutive numbers is divisible by 6.
 
Hope it helps!
Thank you

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