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

Pawan Prajapati , 4 Years ago
Grade 12
anser 3 Answers
Harshit Singh

Last Activity: 4 Years ago

Dear Student

(i) 2 × 3 × 4 = 24 which is divisible by 6
(ii) 5 × 6 × 7 = 210 which is divisible by 6
​
Thanks

Ram Kushwah

Last Activity: 4 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

Last Activity: 3 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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