Question

The sum of three consecutive integers is 84. Find the prime number out of the three.

Answer 1

29 is the prime number in those three.

Step-by-step explanation:

• We assume three prime numbers as x, x + 1, x + 2.

• Since, it is given that their sum is 84. So, we can write as;

• x + x + 1 + x + 2 = 84

                     3x + 3 = 84

                            3x = 81

                              x = 27

Therefore, the numbers are 27, 28 and 29.

• Now, we are going to check that which one is prime.

We pick 27.

• We divide it by 2. We do not get a whole number.

• So, we divide it further, by another prime numbers as 2, 3, 5, 7, 11, 13.....

Here, we get 27 is divisible by 3. So, this is not a prime number.

Then, we pick 28.

• When we divide it by 2, we get the whole number as 14. So, this is not a prime number.

At last, we pick 29.

• We divide it by 2. We don't get a whole number.

• So, we divide it further, by another prime numbers as 2, 3, 5, 7, 11, 13, 17......

Thus, we don't get the whole number.

• Therefore, 29 is a prime number.

Thus, 29 is the prime number in those three.