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The greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1, Is
- a)6
- b)4
- c)16
- d)8
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The greatest number which always divides the product of the predecesso...
3,5,7,9 and so one are other than 1 odd natural number.
Now, the predecessor and successor of 3 are 2 and 4 respectively. The product is ⇒2×4=8
Similarly, the predecessor and successor of 5 are 4 and 6 respectively. The product is ⇒4×6=24 and so on.
Thus, the above shows that greatest number which always divides the product of the predecessor and successor of an odd natural other than 1 is 4
Now, the predecessor and successor of 3 are 2 and 4 respectively. The product is ⇒2×4=8
Similarly, the predecessor and successor of 5 are 4 and 6 respectively. The product is ⇒4×6=24 and so on.
Thus, the above shows that greatest number which always divides the product of the predecessor and successor of an odd natural other than 1 is 4
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Most Upvoted Answer
The greatest number which always divides the product of the predecesso...
Finding the Greatest Number which always divides the product of the predecessor and successor of an odd natural number other than 1
To find the greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1, we need to follow the below steps:
Step 1: Consider an odd natural number other than 1, let's say n.
Step 2: Find the predecessor and successor of n, which are (n-1) and (n+1) respectively.
Step 3: Find the product of (n-1) and (n+1), which is (n^2-1).
Step 4: Factorize (n^2-1) as (n-1)(n+1).
Step 5: Identify the common factors in (n-1) and (n+1).
Step 6: The greatest number which always divides the product of (n-1) and (n+1) is the HCF of (n-1) and (n+1).
Step 7: If (n-1) and (n+1) are both even, then the HCF is 2.
Step 8: If (n-1) and (n+1) are both odd, then the HCF is 2.
Step 9: If either (n-1) or (n+1) is a multiple of 4, then the HCF is 4.
Step 10: If either (n-1) or (n+1) is a multiple of 3, then the HCF is 2.
Step 11: Therefore, the greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1 is 4.
Therefore, option (B) 4 is the correct answer.
To find the greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1, we need to follow the below steps:
Step 1: Consider an odd natural number other than 1, let's say n.
Step 2: Find the predecessor and successor of n, which are (n-1) and (n+1) respectively.
Step 3: Find the product of (n-1) and (n+1), which is (n^2-1).
Step 4: Factorize (n^2-1) as (n-1)(n+1).
Step 5: Identify the common factors in (n-1) and (n+1).
Step 6: The greatest number which always divides the product of (n-1) and (n+1) is the HCF of (n-1) and (n+1).
Step 7: If (n-1) and (n+1) are both even, then the HCF is 2.
Step 8: If (n-1) and (n+1) are both odd, then the HCF is 2.
Step 9: If either (n-1) or (n+1) is a multiple of 4, then the HCF is 4.
Step 10: If either (n-1) or (n+1) is a multiple of 3, then the HCF is 2.
Step 11: Therefore, the greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1 is 4.
Therefore, option (B) 4 is the correct answer.
Community Answer
The greatest number which always divides the product of the predecesso...
Odd number=3
product of precedor and successor =2×4=8
with .minimum odd number of the product is divisible by 8 then for the greater ones,it should be 8
product of precedor and successor =2×4=8
with .minimum odd number of the product is divisible by 8 then for the greater ones,it should be 8
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