Is 119 a prime number?

Steps to Solve

1. Identify the Factors of 119

To determine if 119 is a prime number, we need to find its factors. This involves checking for divisibility by natural numbers starting from 2 up to the square root of 119.

2. Calculate the Square Root of 119

The square root of 119 helps us determine the range of numbers we need to check.

$$ \sqrt{119} \approx 10.9 $$

This means we only need to check for factors up to 10.

3. Check for Divisibility by Each Number

We check each natural number (starting from 2) for whether it divides 119 evenly (no remainder):

• Check 2: $119 \div 2$ (not even, remainder exists)
• Check 3: $119 \div 3 \approx 39.67$ (not divisible)
• Check 4: $119 \div 4 \approx 29.75$ (not divisible)
• Check 5: $119 \div 5 \approx 23.8$ (not divisible)
• Check 6: $119 \div 6 \approx 19.83$ (not divisible)
• Check 7: $119 \div 7 = 17$ (divisible)
• Check 8: $119 \div 8 \approx 14.875$ (not divisible)
• Check 9: $119 \div 9 \approx 13.22$ (not divisible)
• Check 10: $119 \div 10 \approx 11.9$ (not divisible)

4. Conclusion About the Number 119

Since 119 is divisible by 7, we know it has factors other than 1 and itself. Therefore, it is not a prime number.