The average of all prime numbers between 60 to 80 is:
Prime Numbers Average Calculation: 60 to 80
This guide provides a clear, step-by-step method to determine the average of all prime numbers found within the range of 60 to 80.
Prime Number Definition
A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Numbers like 2, 3, 5, 7, 11 are examples of prime numbers.
Prime Numbers in Range 60-80 Identification
First, let's list all the integers from 60 to 80:
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79.
Now, we identify which of these numbers are prime:
- 61: Is prime (divisors: 1, 61).
- 62: Is not prime (divisible by 2).
- 63: Is not prime (divisible by 3, 7).
- 64: Is not prime (divisible by 2).
- 65: Is not prime (divisible by 5).
- 66: Is not prime (divisible by 2).
- 67: Is prime (divisors: 1, 67).
- 68: Is not prime (divisible by 2).
- 69: Is not prime (divisible by 3).
- 70: Is not prime (divisible by 2).
- 71: Is prime (divisors: 1, 71).
- 72: Is not prime (divisible by 2).
- 73: Is prime (divisors: 1, 73).
- 74: Is not prime (divisible by 2).
- 75: Is not prime (divisible by 3, 5).
- 76: Is not prime (divisible by 2).
- 77: Is not prime (divisible by 7, 11).
- 78: Is not prime (divisible by 2).
- 79: Is prime (divisors: 1, 79).
The prime numbers identified between 60 and 80 are: 61, 67, 71, 73, and 79.
Average Calculation Steps
The average (or mean) is found by summing all the numbers and dividing by how many numbers there are.
Sum Calculation
We add the identified prime numbers:
Sum = 61 + 67 + 71 + 73 + 79
Sum = \( 351 \)
Average Calculation
The formula for the average is:
Average = \( \frac{\text{Sum of prime numbers}}{\text{Count of prime numbers}} \)
There are 5 prime numbers in our list.
Average = \( \frac{351}{5} \)
Average = \( 70.2 \)
Final Average Result
The average of all prime numbers between 60 and 80 is calculated to be 70.2.
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