Prime Number worksheet

1. Is it prime? 90 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √90

   $\sqrt{90}$$=9.4868$

2. 2 is the first prime that divides 90 evenly, so 90 has a factor other than 1 and itself

   $90$$=2\times 45$

3. Conclusion

   $\text{90 is not prime}$

2. Is it prime? 110 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √110

   $\sqrt{110}$$=10.4881$

2. 2 is the first prime that divides 110 evenly, so 110 has a factor other than 1 and itself

   $110$$=2\times 55$

3. Conclusion

   $\text{110 is not prime}$

3. Is it prime? 74 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √74

   $\sqrt{74}$$=8.6023$

2. 2 is the first prime that divides 74 evenly, so 74 has a factor other than 1 and itself

   $74$$=2\times 37$

3. Conclusion

   $\text{74 is not prime}$

4. Is it prime? 80 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √80

   $\sqrt{80}$$=8.9443$

2. 2 is the first prime that divides 80 evenly, so 80 has a factor other than 1 and itself

   $80$$=2\times 40$

3. Conclusion

   $\text{80 is not prime}$

5. Is it prime? 66 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √66

   $\sqrt{66}$$=8.124$

2. 2 is the first prime that divides 66 evenly, so 66 has a factor other than 1 and itself

   $66$$=2\times 33$

3. Conclusion

   $\text{66 is not prime}$

6. Is it prime? 105 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √105

   $\sqrt{105}$$=10.247$

2. 3 is the first prime that divides 105 evenly, so 105 has a factor other than 1 and itself

   $105$$=3\times 35$

3. Conclusion

   $\text{105 is not prime}$

7. Is it prime? 115 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √115

   $\sqrt{115}$$=10.7238$

2. 5 is the first prime that divides 115 evenly, so 115 has a factor other than 1 and itself

   $115$$=5\times 23$

3. Conclusion

   $\text{115 is not prime}$

8. Is it prime? 85 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √85

   $\sqrt{85}$$=9.2195$

2. 5 is the first prime that divides 85 evenly, so 85 has a factor other than 1 and itself

   $85$$=5\times 17$

3. Conclusion

   $\text{85 is not prime}$

9. Is it prime? 75 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √75

   $\sqrt{75}$$=8.6603$

2. 3 is the first prime that divides 75 evenly, so 75 has a factor other than 1 and itself

   $75$$=3\times 25$

3. Conclusion

   $\text{75 is not prime}$

10. Is it prime? 140 is not prime

1. Any number that isn't prime has a prime factor no bigger than its square root, so you only need to test the primes up to √140

   $\sqrt{140}$$=11.8322$

2. 2 is the first prime that divides 140 evenly, so 140 has a factor other than 1 and itself

   $140$$=2\times 70$

3. Conclusion

   $\text{140 is not prime}$