Is 1,009 a Prime Number?
Yes, 1,009 is prime. Its only factors are 1 and 1,009, so nothing smaller divides it evenly.
The Square Root Test
You do not need to try every number below 1,009. If 1,009 had a factor larger than its square root, it would also have a matching factor smaller than it, so you only test the primes up to √1,009 ≈ 31.8.
- 1,009 ÷ 2 = 504 remainder 1
- 1,009 ÷ 3 = 336 remainder 1
- 1,009 ÷ 5 = 201 remainder 4
- 1,009 ÷ 7 = 144 remainder 1
- 1,009 ÷ 11 = 91 remainder 8
- 1,009 ÷ 13 = 77 remainder 8
- 1,009 ÷ 17 = 59 remainder 6
- 1,009 ÷ 19 = 53 remainder 2
- 1,009 ÷ 23 = 43 remainder 20
- 1,009 ÷ 29 = 34 remainder 23
- 1,009 ÷ 31 = 32 remainder 17
None of the remainders is 0, so no prime divides 1,009 and it is prime.
What This Means for 1,009
A prime has exactly two factors, 1 and itself. So the factors of 1,009 are 1 and 1,009, and its prime factorization is just 1,009.
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