Is 221 a Prime Number?
No, 221 is not prime. It is divisible by 13, because 221 ÷ 13 = 17. A number with a factor other than 1 and itself is composite.
The Square Root Test
You do not need to try every number below 221. If 221 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 √221 ≈ 14.9.
- 221 ÷ 2 = 110 remainder 1
- 221 ÷ 3 = 73 remainder 2
- 221 ÷ 5 = 44 remainder 1
- 221 ÷ 7 = 31 remainder 4
- 221 ÷ 11 = 20 remainder 1
- 221 ÷ 13 = 17 remainder 0 (divides evenly)
The remainder is 0 for 13, so 13 is a factor. That is enough to show 221 is not prime, so you can stop testing.
Prime Factorization of 221
Keep dividing until every part is prime: 221 = 13 × 17.
Factors of 221
221 has 4 factors: 1, 13, 17, 221.
Check another number
Type any whole number into the Prime Number Checker to see the full test.