Is 77 Prime?
Check if 77 is a prime number. A prime number is only divisible by 1 and itself.
Result:
✗ NO — 77 is NOT a prime number
Step-by-Step Solution
Step 1
What is a Prime Number?
A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.
To check if 77 is prime, we need to verify that no number from 2 to √77 divides it evenly.
Step 2
Determine Testing Range
Since 77 is odd, we only need to check odd divisors.
We only need to test up to √77 ≈ 8.77, which rounds down to 8.
If 77 has a factor larger than √77, it must also have a corresponding factor smaller than √77.
Step 3
Test Odd Divisors
Testing: 3, 5, 7, ... up to 8
77 ÷ 3 = 25 remainder 2
77 ÷ 5 = 15 remainder 2
77 ÷ 7 = 11 (no remainder!)
We found that 7 divides 77 evenly!
Step 4
Conclusion
77 = 7 × 11
Since 77 has factors other than 1 and itself, 77 is NOT a prime number.