Question

product of the predecessor and successor of an odd natural number is always divisible by . . . .
a.2 b.4 c.6 d.8

Answer 1

hey mate
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here is your answer
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Your answer is { 4 }
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solution:-
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let's take 11
Predecessor = 10
Successor = 12
Then 10 × 12 = 120
120/4 = 30
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mark brainliest

Answer 2

Answer:

Product of the predecessor and successor of an odd natural number is always divisible by 2 and 4.

So, option a. 2 and option b. 4  both are correct.

Step-by-step explanation:

• Any odd Natural Number can be written as 2n+1, where n is any natural number(n= 1,2,3,..........).

• Predecessor of (2n + 1) = (2n+1)−1 = 2n

• Successor  of (2n + 1)   = (2n+1) + 1

                     =2n+2

• Product  of the Predecessor and Successor = 2n.(2n+2)

                                                                         =2n.2(n+1)

                                                                         =4.n(n+1)

As n= {1,2,3,4........}

 4.n(n+1) is a natural number and can be expressed as a multiple of 4.

Any multiple of 4 is divided by 2 and 4.

• Hence, product of the predecessor and successor of an odd natural number is always divisible by 2 and 4.

• 1 is also an odd natural number whose predecessor is 0 and successor is 2 . Their product is 0.

     0 divided by any number is 0.