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If the sum of three consecutive odd natural numbers is 69, then the prime number out of these numbers will be ____.

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Detailed Solution

If the sum of three consecutive odd natural numbers is 69, then the prime number out of these numbers will be 23.
We know that natural numbers are the integers that are greater than zero.
So, we'll use the three odd natural integers

x, x + 2

and

x + 4

.
And their sum,

⇒ x + x + 2 + x + 4

As per the question:

⇒ x + x + 2 + x + 4 = 69

⇒ 3 x + 6 = 69

⇒ 3 x = 69 − 6

⇒ 3 x = 63

x = 633

x = 21

Thus, three sequential odd numbers are,

x = 21

x + 2 = 21 + 2

⇒ 23

x + 4 = 21 + 4

⇒ 25

So, the required numbers will be 21, 23 and 25.
Hence, the prime number among these three is 23.
Therefore, 23 is the correct answer.

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